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COMPRESSED AIR 






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PUBLISHERS OF BOOKS FO R_, 

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COMPRESSED AIR 



A TREATISE ON THE PRODUCTION 

TRANSMISSION AND USE OF 

COMPRESSED AIR 



BY 

THEODORE SIMONS, E. M., C. E. 
i 

PROFESSOR OF MINING ENGINEERING, UNIVERSITY OF MONTANA, 

SCHOOL OF MINES; MEMBER AMERICAN INSTITUTE OF 

MINING AND METALLURGICAL ENGINEERS 



Second Edition 



McGRAW-HILL BOOK COMPANY, Inc. 

NEW YORK: 370 SEVENTH AVENUE 

LONDON: 6 & 8 BOUVERIE ST., E. C. 4 

1921 












Copyright, 1914, 1921, by the 
McGraw-Hill Book Company, Inc. 



tf /- W 



FEB 24 m\ 



TSE MAPLE PRESS YORK PA 



§>CI.A605881 



<8 



PREFACE TO SECOND EDITION 

In preparing a second edition of this book, its character as an 
elementary treatise on the principles of Compressed Air has 
been maintained throughout. To bring the subject up-to-date, 
however, the greater portion of the chapter on Transmission has 
been re-written. Modern formulas were introduced with ex- 
amples of their application. The important effect of altitude 
differences on Compressed Air installations has been illustrated 
by reference to new equations in Article 4 and by the example 
under Article 97. A new Table VIII, containing the principal 
Compressed Air formulas was substituted for the old table that 
has become superfluous. The obsolete Hurricane valve in 
Article 147 has been replaced by a description of the modern 
Ingersoll-Rogler valve. 

Altogether, a general revision of the original text and the 
addition of new material brings the second edition of the book 
abreast of modern theory and practice. 

Theodore Simons. 

Butte, Montana, 

December, 1920. 



PREFACE TO FIRST EDITION 

This treatise is intended to give the student and the general 
reader such an insight into the natural laws and physical prin- 
ciples underlying the production, transmission and use of com- 
pressed air, as shall enable him to comprehend the operation of 
the various appliances employed for this purpose and to judge 
of their merit. 

No attempt has been made to present in this book an extensive 
description of all the existing types of compressors or of the count- 
less appliances using compressed air. The author's chief aim 
was to provide the student, who is interested in technical ques- 
tions concerning the operation as well as the construction of 
compressors and air engines, with a background of understand- 
ing that will enable him, not only to solve the many theoretical 
problems connected therewith, but to make independent research 
into the seemingly unlimited possibilities of compressed air. 
The territory still unexplored is vast and full of promises to the 
intrepid explorer who enters the field with a thorough knowledge 
of all the truths discovered, as well as the pitfalls encountered, 
by those who have gone before him. 

The numerous, carefully selected problems constitute what 
the author believes to be one of the strong features of this book. 
If ever any doubt lingers in the student's mind as to the mean- 
ing of certain principles or laws presented in the text and their 
practical application, a numerical problem will, as a rule, re- 
move the doubt and make clear the meaning. Moreover, such 
problems make the student familiar with actual quantities, never 
revealed by mere formulas; quantities which are often startling 
to the uninitiated and impress him with the practical value of 
such formulas more forcibly then the mere text can do. 

The author has endeavored to bring the work well within 
the comprehension of the average technical student who has a 
sound knowledge of the elements of algebra, physics and me- 
chanics. Higher mathematics were used sparingly and only 
when they led to a simpler solution of certain problems. To the 
advanced reader some of the deductions contained in the book 

vii 



viii PREFACE 

may appear unnecessarily lengthy. It has been the writer's 
experience, however, that many of the difficulties encountered 
by students arise from a misunderstanding of facts which, al- 
though perfectly obvious to one who has mastered the subject, 
remain nevertheless obscure to the beginner unless explained 
from various points of view and by analogy with facts already 
familiar to him. 

In preparing this treatise the writer has made free use of the 
rather scattered and by no means voluminous literature on the 
subject of compressed air. His debt to all who have labored in 
this field before him can hardly be acknowledged adequately 
by the mere mentioning of their names. He has therefore re- 
frained from referring in the text to such names but wishes to 
express in this preface his gratitude to all authors and investi- 
gators from whose writings he has drawn both inspiration and 
information. 

Throughout the preparation of this work the author had the 
untiring assistance of President C. H. Bowman of the Montana 
State School of Mines, whose constructive criticism and sugges- 
tions, based on a vast theoretical knowledge and practical ex- 
perience, were of inestimable value. To him the author is in- 
debted to an extent that the mere mentioning of the fact can 
scarcely requite. 

For permission to use diagrams, illustrations, tables and other 
data, contained in the bulletins of manufacturers, the author is 
indebted to the following firms: Allis Chalmers Company, 
Ingersoll Rand Company, Nordberg Manufacturing Company, 
Norwalk Iron Works Company, Sullivan Machinery Com- 
pany, The Laidlaw-Dunn-Gordon Company and Union Steam 
Company. 

Theodore Simons. 
Butte, Montana, 
April, 1914. 



CONTENTS 



Page 

Preface v 



PART I 
The Production of Compressed Air 

CHAPTER I 

The Physical Properties of Air. Definition of Terms used in 
Discussing Compressed-air Problems 

1. Composition of air. 

2. Weight of air. 

3. Atmospheric pressure. 

4. Formulas for calculation of atmospheric pressure and altitudes. 

5. General effect of heat on air. 

6. Specific heat and the B.T.U. 

7. Specific heat of air at constant volume. 

8. Specific heat of air at constant pressure. 

9. Absolute zero. 

10. Absolute temperature. 

11. Gage and absolute pressure. 

12. Free air. 

13. Isothermal compression and expansion. 

14. Adiabatic compression and expansion. 



CHAPTER II 

Behavior of Air Undergoing Compression and under the Appli- 
cation of Heat 

15. Boyle's or Mariotte's law. 

16. Boyle's or Mariotte's second statement. 

17. Charles' or Gay Lussac's law. 

18. Charles' or Gay Lussac's second statement. 

19. Charles' or Gay Lussac's third statement. 

20. Boyle's and Charles' laws combined. 

21. Weight of equal volumes of air at constant pressure and vary- 

ing temperature. 

22. Weight of equal volumes of air at constant temperature and 

varying pressure. 

23. Weight of one cubic foot of air at atmospheric pressure and at 

any temperature. 

24. Weight of one cubic foot of air at any absolute pressure and 

any absolute temperature. 
24a. Application of weight-formulas to altitudes. 

ix 



X CONTENTS 

CHAPTER III 

Page 
The Compression of Air in Air Compressors 14 

25. Air cylinders of a compressor. 

26. Waterjackets. 

27. Inlet and discharge valves in general. 

28. Analysis of single-stage compression. 

29. Receiver pressure. 

CHAPTER IV 

Theory of Air Compression 17 

30. Theory of isothermal compression. 

31. Graphical illustration of isothermal compression. 

32. Construction of isothermal compression curve. 

33. Work of isothermal, single-stage compression and delivery. 

34. Net work per stroke, isothermal compression. 

35. Net work, formula. 

36. Mean gage pressure, isothermal compression and delivery. 

37. Horse-power, isothermal, single-stage compression and delivery. 

38. Isothermal compression not attainable in practice. 

39. Isothermal expansion formulas. 

40. Theory of adiabatic compression. 

41. Relation between temperature, volume and pressure in adia- 

batic compression and expansion. 
41a. Law of thermodynamics applied to adiabatic compression 
and expansion. 

42. Graphical illustration, adiabatic compression. 

43. Construction of adiabatic compression curve. 

44. Work of adiabatic, single-stage compression and delivery. 

45. Net work per stroke. 

46. Mean gage pressure, adiabatic, single-stage compression 

and delivery. 

47. Horse-power, adiabatic, single-stage compression and delivery. 

48. Horse-power in terms of weight and temperature. 

49. Relation between final pressure and power required to compress 

to that pressure. 

50. Modified power values for practical computations. 

CHAPTER V 

Clearance, Volumetric Efficiency, Capacity, Speed, Mechanical 

Efficiency of Compressors 38 

51. Clearance explained. 

52. Losses due to clearance. 

53. Volumetric efficiency of a compressor. 

54. Capacity of a compressor. 

55. Speed of a compressor. 

56. Mechanical efficiency of a compressor. 

CHAPTER VI 

Two-stage and Multi-stage Compression, also Known as Com- 
pound Compression 43 

57. Theory of compound or multi-stage compression. 

58. Analysis of two-stage compression. 

59. Ratio of compound compression. 

60. Ratio for two-stage compression. 

61. Ratio for three-stage compression. 

62. Ratio for four-stage compression. 



CONTENTS xi 

Page 

63. Cylinder diameters of compound compressors. 

64. Cylinder diameters of two-stage compressors. 

65. Cylinder diameters of three-stage compressors. 

66. Cylinder diameters of four-stage compressors. 

67. Volumetric efficiency of compound compressors. 

68. Horse-power, two-stage compression and delivery. 

69. Horse-power formula, two-stage compression and delivery. 

70. Horse-power formula, three-stage compression and delivery. 

71. Horse-power formula, four-stage compression and delivery. 

72. Mean gage pressure, two-stage compression and delivery. 

73. Mean gage pressure, three-stage compression and delivery. 
73a. Final volumes and temperatures — stage compression. 

74. Modified power values for practical problems. 

75. Advantages of compound compression. 

76. When to use compound compression. 

CHAPTER VII 

Effect of Altitude on Air Compression 60 

77. Volumetric efficiency at altitudes. 

78. Multipliers for altitude computations. 

79. Power required for compression at altitudes. 

80. Stage compression at high altitudes. 

81. Advantage of stage compression at altitudes. 

CHAPTER VIII 

The Compressed Air Indicator Card 64 

82. Air cards, explanation, description and interpretation. 

83. Air card of single-stage compressor. 

84. Air card of two-stage compressor. 

85. Air card of two-stage Nordberg compressor. 

CHAPTER IX 

Cooling Water Required in Compression; Efficiency of Com- 
pressor Plant; Air-compressor Explosions 71 

86. Amount of cooling water required in compression. 

87. Efficiency of a compressor plant. 

88. Compressor explosions. 

89. Dangerous effect of throttling devices. 

90. Prevention of explosions. 



PART II 
The Transmission of Compressed Air 



CHAPTER X 

Transmission of Compressed Air 85 

91. Conveyance of compressed air in iron pipes. 

92. Laws governing flow of compressed air in iron pipes. 

93. Loss of pressure or head in air transmission. 

94. Loss of power in air transmission. 




xii CONTENTS 

CHAPTER XI 

Page 
Dimensions op Pipe Lines for Conveying Compressed Air 88 

95. Dimensions of pipe line in general. 

96. Formulas for pipe line computations. 

97. Effect of altitude on air transmission. 

98. Dimensions of branch pipes. 

99. Effect of bends and elbows in pipe line. 

100. Velocity of air in pipe line. 

100a. The planning of a transmission line. 

101. Pipe line efficiency. 

101a. Resume of pipe line computations. 

102. Effect of altitude on pipe line efficiency. 

103. Final dimensions of pipe lines. 

104. Pipe line construction. 

105. Flow of compressed air from an orifice. 

PART III 
The Use of Compressed Air 

CHAPTER XII 

Theory of Air Engines 105 

106. Compressed air to drive engines. 

107. Compressed air used at full pressure. 

108. Work performed by engines using air at full pressure 

109. Efficiency of engines using air at full pressure. 

110. Work of air used with complete adiabatic expansion. 

111. Horse-power developed by air used with complete expansion. 

112. Complete expansion not practicable 

113. Work of air used with partial expansion. 

114. Mean gage pressure partial expansion. 

115. Horse-power, partial expansion. 

116. Modified power values for practical computations. 

CHAPTER XIII 

Effect of Loss of Heat, Generated During Compression, on the 
Ultimate Useful Energy Residing in a GrvEN Quantity 
of Compressed Air 113 

117. Effect of heat loss on energy in air. 
117a. Determination of the value of "n". 

CHAPTER XIV 

Internal or Intrinsic Energy of Air 121 

118. Internal or intrinsic energy of air. 

119. Intrinsic energy of atmospheric air at 60° Fahr. 

120. Intrinsic energy of air at 100 lb. gage and at 60° Fahr. 

CHAPTER XV 

The Efficiency of a Compressed-air System 124 

CHAPTER XVI 

Reheating of Compressed Air 126 

122. Reheating of compressed air. 

123. Sullivan air reheater. 

124. Sergeant air reheater. 

125. Other reheaters. 



CONTENTS xiii 

PART IV 

Air Compressors and Accessories 

CHAPTER XVII 

Page 
Examples of Modern Air-Compressors of the Reciprocating Type. 132 

126. Examples of modern air compressors. 

127. Outline diagram of steam-driven compressors. 

128. Operation of steam-driven, straight-line compressors. 

129. Sullivan straight-line, steam-driven, single-stage compressor. 

130. Sullivan straight-line, steam-driven, two-stage compressor. 

131. Operation of steam-driven duplex compressors. 
131a. Disadvantages of duplex compressors. 

132. Laidlaw-Dunn-Gordon duplex, steam-driven, single-stage com- 

pressor. 

133. Ingersoll-Rand duplex, steam-driven, two-stage compressor. 

134. Allis-Chalmers duplex, steam-driven, two-stage compressor. 

135. Other types of steam-driven compressors. 

136. Power-driven compressors. 

137. Belt-driven compared with steam-driven compressors. 

138. Norwalk belt-driven two-stage compressor. 

139. Norwalk compressor with direct water-wheel drive. 

140. Electrically-operated compressors. 

141. Nordberg electrically-driven, geared two-stage compressor. 

142. Ingersoll-Rand direct-connected, electrically-driven two-stage 

compressor. 

CHAPTER XVIII 

Important Mechanical Features of Air Compressors 1.48 

143. Important mechanical features of air compressors. 

144. Inlet valves in general. 

145. Poppet inlet valves. 

146. Inlet valves of the Corliss type. 

147. Ingersoll-Rogler valve. 

148. Discharge valves in general. 

149. Poppet discharge valves. 

150. Mechanically moved discharge valves. 

151. Allis-Chalmers mechanically moved discharge valve. 

152. Nordberg mechanically moved discharge valve. 

153. Corliss discharge valves not always applicable. 

154. Intercooler. 

155. Design of inter-cooler. 

CHAPTER XIX 

Compressor Accessories 155 

156. Compressor accessories. 

157. Automatic regulators. 

158. Air cylinders unloaders. 

159. Combined speed-governor and air-pressure regulator. 

160. Ingersoll-Rand regulator. 

161. Air receivers. 

162. After-coolers. 

APPENDIX 

Tables I to IX 161 

Index 169 



PART 1 

THE PRODUCTION OF COMPRESSED AIR 




COMPRESSED AIR 



CHAPTER I 

THE PHYSICAL PROPERTIES OF AIR. DEFINITION OF 

TERMS USED IN THE DISCUSSION OF COMPRESSED 

AIR PROBLEMS 

1. Composition of Air. — Air is chiefly composed of the ele- 
ments oxygen and nitrogen. By weight the proportions are 
about 23 parts of oxygen and 77 Darts of nitrogen. By volume 
the proportions are about 21 parts of oxygen and 79 parts of 
nitrogen. 

2. Weig.it of Air. — By actual measurement it has been found 
that 1 cu. ft. of air at atmospheric pressure at sea level and at 
60° Fahr. weighs 0.0764 lb. Since the density of air changes 
with the pressure and with the temperature, it follows that the 
weight of a given volume of air varies with pressure and tem- 
perature. How this weight can be computed when pressure and 
temperature are known is shown in Articles 21 to 24. 

3. Atmospheric Pressure. — Since air has weight, it is evident 
that the enormous quantities of air that constitute the atmos- 
phere must exert a considerable pressure upon the earth. 

By experiment the atmospheric pressure at sea level, with 
the barometer at 30 in. and a temperature of 32° Fahr., has been 
found to average 14.7 lb. per square inch above vacuum. 

4. Air Pressures at Varying Altitudes and Temperatures. — 
The solving of many compressed-air problems requires a knowl- 
edge of the pressure at any point of a vertical column of free or 
compressed air. Without having recourse to actual measure- 
ments, these pressures may be calculated as follows : 

Let Fig. \A represent an air column having a base 1 sq. in. in 
area and a height of h feet. 

1 



COMPRESSED AIR 



dh 



Let Pi and P 2 = absolute pressures per square inch at bottom 

and at top of column, respectively. 
P x = absolute pressure at a point x ft. 
above bottom, in pounds per 
P x square inch. 

w x = weight in pounds of one cubic 

foot of air at point x. 
P a = atmospheric pressure at sea level 

(14.7 lb.). 
w a = weight in pounds of one cubic 
p i foot of atmospheric air at sea level 

and at an absolute temperature 



Fig. la. 

Then the absolute pressure at a point dh ft. below x will be 
P x -\-dP x lb. per sq. in. 



in which dP x = weight in pounds of shaded air column. 



But 
whence 



dP x = — 7-7 dhw x lb. 



dh = 14A 



dP.. 



W; 



(1) 



From Art. 22 — =^ 

W a Pa 



whence 



whence 



P x 

w x = Wap £ - Introducing in (1) gives 

■La 

^ = 144— a ^ 

Wa Px 



h = 144 






(2) 



From Art 22 the weight of one cubic foot of atmospheric air at 
sea level and at an absolute temperature T a is 
39.804 



w„ = 



T a 



lb. 



(3) 



Introducing (3) in (2) and using common logarithms, gives 

14 IT 

ft = 144 ,L'L, a X 2.302 (logPi-logP 2 ) 



39.804 
whence log P 2 = log Pi 



122.4 (degree F.+461) 



(4) 



THE PHYSICAL PROPERTIES OF AIR 2a 

For an average temperature of 60° Fahr. equation (4) becomes : 

log P 2 = log Pi - 0.0000157/1 (5) 

whence log Pi = log P 2 +0.0000157/i (6) 

«* *- 10 oS^ 1 i 57 p, - fl8roh *F: (7) 

Example 1. — Atmospheric pressure Pi at sea level is 14.7 lb. What 
is atmospheric pressure P 2 at an elevation of 5000 ft. above sea level 
and at a temperature of 60° Fahr.? 

1 D 1 1A>7 5000 

log P 2 = log 14.7 — 



122.4(60+461) 
P 2 = 12.27 lb. per. sq. in. 

Example 2. — By barometric observation the atmospheric pressure 
at a certain mine was found to be 11.24 lb. per sq. in. Average tem- 
perature 60° Fahr. What is the elevation of the. mine above sea level? 

From equation (7) 

h = QS70 log 5^ = 7400 ft - 

Example 3. — A compressor at a line, located 5500 ft. above sea level, 
furnishes compressed air for air-drills at the bottom of a shaft 2800 ft. 
deep. A pressure gage in the pipe line, near the shaft bottom reads 
60 lb., when the air is not moving. 

(a) What is the absolute pressure corresponding to this gage pressure? 

(b) What should be the reading of a pressure-gage in the pipe line 
at the collar of the shaft and at the same instant? 

Solution (a). Elevation of shaft bottom above sea level is 5500 — 
2850 = 2650 ft. 

Atmospheric pressure at shaft bottom 

logP 2650 = log 14.7-0.0000157X2650 
whence P 266 o - 13.36 lb. 

Added to 60 lb. gives absolute pressure of compressed air at shaft 
bottom 

Pi = 60+ 13.36 = 73.36 lb. abs. 



26 COMPRESSED AIR 

Solution (6). Atmospheric pressure at shaft collar: 

logP 550 o = log 14.7-0.0000157X5500 
whence P 5 5oo = 12.05 lb. 

Absolute pressure of compressed air at shaft collar: 

logP 2 = log 73.36-0.0000157X2850 
whence P 2 = 66.2 lb. abs. 

Gage pressure 66.20-12.05 = 54.15 lb. gage. 

In well-regulated practical operations such readings are taken 
frequently and at various points in the transmission line. A 
marked discrepancy between the actual and the computed 
readings indicates trouble in the pipe line such as leaks or care- 
less waste of air. The cause of the discrepancy is then traced 
to its source and the proper remedies are applied before much 
harm is done. 

5. General Effect of Heat on Air. — Heat has a tendency to 
increase the volume of air, that is, to expand it. If air at out- 
side temperature is confined within a closed cylinder, and then 
heated, the result of this tendency to expand may be two-fold : 

1. If the cylinder is tightly closed at both ends, and if the 
walls are strong enough to resist deformation, the volume of air 
will remain constant and its pressure will increase. 

2. If in the upper end of the cylinder we insert a piston which 
is free to move in the cylinder and has a certain weight, it will 
descend in the air-filled cylinder until its weight is balanced by 
the pressure of the confined air. 

If now the air in this cylinder is heated, it expands and the 
piston will start upward, and will stop when the expansion has 
ceased; in this case, the load of the piston and consequently the 
pressure of the air have remained the same as before heating, 
but the volume has increased. 

The effect of heat upon the air in the cylinder is, therefore, in 
the first case, to increase its pressure under constant volume; 
and in the second case, to increase the volume under constant 
pressure. 

Reversely, if we teke a closed cylinder full of hot air and allow 



THE PHYSICAL PROPERTIES OF AIR 3 

it to cool, the volume of this air will, of course, remain the same, 
but its pressure will fall gradually, until it becomes the same as 
it was before heating. 

In a similar way, if we allow the heated air in the cylinder 
with its piston to cool, the volume of air confined under the piston 
will shrink, and the piston will gradually descend to the point 
where it was before the air was heated, the pressure, of course, 
remaining constant. 

The effect of abstracting heat from the air in the cylinder is, 
therefore, in the first case, to decrease the pressure under con- 
stant volume; and in the second case, to decrease the volume 
under constant pressure. 

6. Specific Heat and The British Thermal Unit.— The specific 
heat of a body is the ratio between the amount of heat required 
to raise the temperature of that body 1 degree and that required 
to raise the temperature of an equal mass of water 1 degree. 

In engineering problems the British Thermal Unit (B.T.U.) 
is usually employed as the unit of heat. It is the quantity of 
heat required to raise the temperature of 1 lb. of water 1° Fahr. 
Thus, the specific heat of water is 1, and the specific heat of any 
substance is the number of B.T.U.'s required to raise the tem- 
perature of 1 lb. of that substance 1° Fahr. 

By a law of thermodynamics, heat and mechanical energy 
are mutually convertible, and heat requires for its production, 
and produces by its consumption, a definite amount of work for 
each thermal unit. 

The mechanical equivalent of the British Thermal Unit has 
been found to be very close to 778 ft.-lb. This value will be 
used throughout this treatise. 

Thus: 1 B.T.U. = 778 ft.-lb. 

7. Specific Heat of Air at Constant Volume. — If heat is applied 
to air contained in a closed vessel, the air is said to be heated under 
constant volume. In this case the number of heat units required 
to raise the temperature of 1 lb. of air by 1° Fahr. is the specific 
heat of air at constant volume. 

Expressed in B.T.U.'s it is: C v = 0.1689 B.T.U.'s. 
Expressed in foot-pounds it is: K v = C v X778 = 131.6 ft.-lb. 

8. Specific Heat of Air at Constant Pressure. — If heat is applied 
to air in a cylinder having a movable piston under a constant 



4 COMPRESSED AIR 

external pressure, the volume increases, and therefore work is 
done in pushing the piston out against the external pressure. 
The number of heat units required in this case to raise the tem- 
perature of 1 lb. of air by 1° Fahr. is the specific heat of air at 
constant pressure. 

Expressed in B.T.U.'s it is: C p = 0.2375 B.T.U.'s. 
Expressed in foot-pounds it is : K P = C P X 778 = 184.8 f t.-lb. 

C p is greater than C v owing to the extra heat required to do the 
work of moving the piston against the external resistance, in 
addition to raising the temperature of the air. Theory indi- 
cates, and experiment shows, that the excess of heat (K p —K v ) 
required in the latter case is equal to the amount of work done 
by the air in expanding against a constant pressure. 

The above specific heats are for dry air. They will be used 
throughout this treatise, although the presence of moisture in the 
air slightly modifies these values. 

9. Absolute Zero. — Direct experiment, in which air at constant 
pressure was exposed to various temperatures, has shown that 
the volume which it occupies at a temperature of 32° Fahr. 
increases or decreases by 1/493 of this volume for each increase or 
decrease of 1° Fahr. 

From this it follows that air heated under constant pressure to a 
temperature of boiling water (212° Fahr.) has increased in 

volume by — t^ — = Zqq = 0-366 or 36 per cent, of the volume 

it occupied at 32° Fahr. The same air at 493° below the freezing 
point of water or 461° below 0° Fahr. would have shrunk 

ky — Zoo — = Zoq °f ^ s v °l ume > or by that volume itself. The 
temperature at which this is assumed to take place is called "the 
absolute zero." For ordinary compressed air problems it is taken 
as 461° below 0° Fahr. This value is used throughout this 
treatise. 

10. Absolute Temperature. — Absolute temperature is the 
temperature above the absolute zero. It is usually designated 
by T while temperatures in degrees Fahr. are designated by t. 
At 60° Fahr. the absolute temperature T is 60°+ 461° = 521°. 
At 0° Fahr. the absolute temperature T is 0°-r-461 o = 461°. At 
-30° Fahr. the absolute temperature is -30°+461 o = 431°. 



THE PHYSICAL PROPERTIES OF AIR 5 

11. Gage and Absolute Pressures. — Ordinary gages register 
pressures above atmosphere. Thus, if the air gage of a com- 
pressor shows 80 lb. pressure, it indicates that the pressure of the 
compressed air is 80 lb. per square inch above the pressure of the 
atmosphere. To find the absolute pressure of air compressed 
at sea level to 80 lb., we must add 14.7 to the gage reading; thus 
80+14.7 = 94.7 lb. absolute. The pressures indicated by the 
gage are called gage pressures; pressures above vacuum are 
called absolute pressures. To obtain absolute pressure at any 
altitude, add atmospheric pressure at that altitude to the gage 
pressure. 

From Table VI atmospheric pressure at 10,000 ft. elevation is 
10.07 lb. per square inch. Hence a gage pressure of 100 lb. at an 
altitude of 10,000 ft. is equal to 100+10.07 = 110.07 lb. absolute 
pressure. 

12. Free Air. — Free air is a term constantly used in dealing with 
problems of air compression. It is air at normal atmospheric 
pressure as taken into the cylinder of a compressor. 

13. Isothermal Compression or Expansion of Air. — From 
experiment we find that heat is generated in the act of compress- 
ing air. If during compression the air could be kept at constant 
temperature by the abstraction of heat as fast as it was generated, 
the air would then be said to be compressed isothermally. 

In expanding against an external resistance, the air gives up, 
or, to speak more correctly, converts heat into mechanical 
energy. If as much heat could be supplied and as fast as it is 
consumed, the air would be said to expand isothermally. In 
isothermal compression or expansion the air remains at constant 
temperature throughout the operation. 

14. Adiabatic Compression or Expansion. — If during com- 
pression the air neither loses nor gains heat, the heat generated 
by the compression remaining in the air and increasing its 
temperature, then the air is said to be compressed adiabatically. 
When the compressed air is allowed to expand against an ex- 
ternal resistance its temperature falls, and if the air during this 
operation receives no heat from without, it is said to expand 
adiabatically. 



CHAPTER II 

BEHAVIOR OF AIR UNDERGOING COMPRESSION AND UNDER 
THE APPLICATION OF HEAT 

There are two fundamental laws governing the behavior of 
air undergoing compression and under the application of heat. 
These laws express the relations existing between volume, 
pressure and temperature. 

15. Boyle's or Mariotte's Law. — The temperature remaining 
constant, the volume of a given weight of air varies inversely as 
the absolute pressure. 

T\ P 

^^ or :P 1 V l =PV 

whence V\ = Vjr- 

V 

and Pi=Pyt 

I i 

in which V = volume of a given weight of air at an absolute 
pressure P. 
Vi = volume of the same weight of air at the same 
temperature and at any absolute pressure Pi. 

Example. — One-hundred cubic feet of free air, compressed isother- 
mally at sea level to 60 lb. gage will occupy a volume: 

100X14.7 1QR ~ f . 

Tl= 6o+ny =19 - 68cu - ft - 

Conversely, 19.6S cu. ft. of air at 60 lb. gage, when expanded isother- 
mally down to atmospheric pressure, will occupy a volume: 

y = V,P, = 19.68(60+ 14.7) =1QOcuft 
P 14.7 

16. Boyle's Law may also be expressed as follows: The tem- 
perature remaining constant, the product of the pressure P 
and the volume V is a constant. 

Pr = PiT~i = constant 
6 



AIR UNDERGOING COMPRESSION AND HEATING 7 

Example. — It has been found that at sea level 1 lb. of air at atmos- 
pheric pressure and at 32° Fahr. occupies a volume of 12.387 cu. ft. 
If we let P = absolute pressure in pounds per square foot 

V = volume of air in cubic feet 
Then for P = (14.7X144) =2116.8 lb. per square foot 
and V = 12.387 cu. ft, 

PV = 2116.8X12.387 = 26,220, nearly. 
If the pressure is increased under constant temperature to two atmos- 
pheres or 29.4 lb. absolute per square inch, the volume of the pound of 
air will have been reduced to one-half of the original volume. We will 
then have: 

Pi = (29.4X144) =4233.6 lb. per square foot 

7i = 12.387X1/2 = 6.1935 cu. ft. 
whence P l V 1 = 4233.6X6.1935 = 26,220 
and PV = P\Vi = constant 

17. Charles' or Gay Lussac's Law. — If the pressure remains 
constant, every increase of temperature of 1° Fahr. produces in a 
given quantity of air an expansion of 1/493 of the volume it 
occupies at a temperature of 32° Fahr. 

V^Vil+at ) 

in which V x = volume of a given weight of air at f Fahr. 
above the freezing point. 
V = volume of same weight of air at freezing point (32° 

Fahr.). 
t = number of degrees rise in temperature above 

freezing point. 
a = coefficient of expansion = 1/493. 

Example. — One pound of atmospheric air at 32° Fahr. at sea level 
occupies a volume V= 12.387 cu. ft. At a temperature of 62° Fahr. 
and at the same absolute pressure it would occupy a volume: 

Fi = 12.387 (1+^X30) = 13.141 cu. ft. 

18. Charles' Law may also be expressed as follows: Under 
constant pressure the volume which a given weight of air occupies 
at different temperatures, varies directly as the absolute tem- 
peratures. 

Let V = volume of a given weight of air at an absolute pressure 
P and an absolute temperature T. 
Vi = volume of the same weight of air at the same absolute 
pressure P and at any absolute temperature TV 



V ' 




Vr- 


T 


T, 


V 



8 COMPRESSED AIR 

Then 



whence 

and 

Example. — One pound of air at 32° Fahr. and at atmospheric pres- 
sure at sea level occupies a volume V— 12.387 cu. ft. At a temperature 
of 62° Fahr. and at atmospheric pressure it would occupy a volume: 

T/ VT 1 12.387(461 + 62) 1Q , . 1 .. 
V * = -T= 461+32 -^ =13 ' 141 CU ' ft - 

Column 2 of Table II gives the volume in cubic feet occupied by 
1 lb. of air at various temperatures, at sea level. 

19. Another deduction may be made from Charles' Law as 
follows: If a certain weight of air be heated to different tem- 
peratures in a closed cylinder so that its volume remains constant, 
the absolute pressures vary directly as the absolute temperatures. 

Pi~Ti 

T 
whence Pi =P ^ 

and Ti = T^ 

Example. — Let absolute pressure of a volume of free air at a tempera- 
ture of 62° Fahr. be 14.7 lb. per square inch. If heated to a temperature 
of 200° Fahr. without changing its volume, the absolute pressure of 
the heated air would be: 

p 1 = Py= u - 7 >< 2 Q2+m = 18 - 58 lb * absolute or 3 - 88 lb - g a s e - 

20. Boyle's and Charles' Laws Combined. — Given a quantity 
(weight) of air which has a volume V, a pressure P, and a tem- 
perature T, we can change it to a condition in which its volume 
is V h its pressure P h and its temperature TV First: Change 
the pressure from P to Pi under constant temperature T, then 
find the new volume V n from Boyle's Law: 

— =— (1) 

V P! U; 



AIR UNDERGOING COMPRESSION AND HEATING 9 

Second: Change the temperature of this volume V n from T 
to T\ under constant pressure Pi. Then find the new volume 
Vi from Charles' Law: 

Multiplying equations (1) and (2) we get: 

VnVl PTj 
V n V P,T 

Whence P^V^PV^ (3) 

In Article 16 it was shown that for 1 lb. of air at 32° Fahr. 
and at atmospheric pressure: 

PV = 26,220 

Substituting this value in equation (3) we get: 

26 220 
PlFl = 32+461 Tl = 53 ' 2 Tl nearly (4) 

The equation is usually written: 

PV = RT ovPxV^RTx (5) 

in which 

P and Pi = absolute pressures in pounds per square foot 

V = volume in cubic feet which 1 lb. of air occupies at 
a temperature of 32° Fahr. and at atmospheric 
pressure (14.7 lb.) 
Vi= volume in cubic feet which 1 lb. of air occupies 
at an absolute pressure Pi and an absolute tem- 
perature Ti 
R = constant = 53.2. 

From equation (5) we deduce: 

Vi Pi 

If this volume of air be raised 1° in temperature at constant 
pressure, its volume will become: 

v «(r,+i) 



10 COMPRESSED AIR 

The change of volume will be: 

v 2 -v 1 =—p i -j^ 

whence P 1 (V 2 -V 1 )=R(T 1 + 1-T 1 )=R (6) 

The first term of the equation is the work done by the pound 
of air in expanding against a constant pressure Pi while the 
temperature of the air is rising 1 degree. In Article 8 it was 
stated that this work is equal to the difference in the specific 
heats, expressed in foot-pounds. 
Hence we may write: 

R = (K P -K V ) = 184.8- 131.6 =53.2 (7) 

which is the same as the value deduced in equation (4). 

Example. — One pound of air at 32° Fahr. (!T = 461+32) and at atmos- 
pheric pressure P (14.7) occupies a volume 7=12.387 cu. ft. 

If we compress this pound of air under constant temperature T to 
100 lb. gage (Pi = 114.7 lb.) we find the new volume V n from equation (1). 

Vn = 12.387 J^ = 1.588 cu. ft. 

If we heat this volume V n of air, which still weighs 1 lb., from 32° Fahr. 
to 150° Fahr. (!Ti = 461 + 150) under constant pressure, we find the new 
volume Vi from equation (2) : 

7i = 1.588X 4 4 6 6 \^3 5 2 ° = 1.967 cu. ft. 

Expressing Pi in pounds per square foot = 144X114.7 = 16,517 lb. 

We get PiFi = 16,517Xl. 97 = 32,500 

The same result could have been obtained directly from equation (4) 

Pi7i = 53.2 T 1 

Pi7 x = 53.2 (150+461) =32,500 
In employing formulas (4) and (5) of this article, it must be borne 
in mind that the pressures are expressed in pounds per square foot, and 
that the quantity of air contained in the volume is 1 lb. 

WEIGHT OF AIR 

21. Weight of Equal Volumes of Air at Constant Pressure 
and Varying Temperatures. — Let a cylinder (Fig. 1 a) with a 
movable piston, be filled with a given weight of air at an absolute 
temperature T and an absolute pressure P in pounds per square 
inch, occupying a volume V a . 



WEIGHT OF AIR 



11 



If heat is applied to the cylinder (a) the air in it will expand 
under constant pressure and the piston will assume the position 
shown in Fig. 1 b. The weight of this air has remained the same 
and so has the pressure, but the volume and the absolute tempera- 
ture have increased, while the density of the mass of air has 
decreased. 

If we now cut off from Fig. 16a volume equal to the volume 
V a in Fig. 1 a it is evident that the weight Wi of the volume V a 
in cylinder (6) is less than the weight of volume V a in cylinder (a). 













mil 


ill 




VOLUME = Va 
ABSOL. PRESS.= P 
AB80L. TEMP.=T 
WEIGHT = W 


a 





VOLUME = Va 
ABSOL. PRE88.= P 
ABSOL. TEMP. =Tl 
WEIGHT = Wjl 

Fig. 1. 



VOLUME = Vj 
^ABSOL. PRESSFp 
ABSOL. TEMP.=Tl 
WEIGHT = W 



This shows that of two equal volumes of air having the same 
absolute pressure, the one having the higher temperature has 
the less weight. The exact relation may be derived from the 
equations in Article 18. It is stated as follows: 

The weight of two equal volumes of air, having the same 
absolute pressure, varies inversely as the absolute temperatures. 

Wx"T 

in which W = weight of a given volume of air at an absolute 
temperature T 
Wi = weight of an equal volume of air at an absolute 
temperature T\ 

22. Weight of Equal Volumes of Air at Constant Temperature 
and Varying Pressures. — Let a cylinder (Fig. 2 b) having a 
movable piston be filled with a given weight of air occupying a 
volume V b and having an absolute pressure P and an absolute 
temperature T. 

If we load the piston with an additional weight (m), the 
piston will descend in the cylinder to the position shown in 
Fig. 2 a. The weight of the air in cylinder (a) has remained 



12 



COMPRESSED AIR 



the same, and the absolute temperature is assumed to have also 
remained the same. But the absolute pressure has increased 
and with it the density of the air. 

If we now cut off from the cylinder (6) a volume V a equal to 
the volume in cylinder (a), it is evident that the weight of volume 
V a in cylinder (6) is less than the weight of volume V a in cylinder 
(a) . This shows that of two equal volumes of air having the same 
absolute temperature, the one having the less pressure has the less 
weight, and vice versa. The exact relation may be derived from 
the equations in Article 15. It is stated as follows: 



VOLUME = \'l 
ABSOL. PRESSpP 
ABSOL. TEMP.=T 
WEIGHT = W 



. v 1 

VOLUME 



Va 

ABSOL. PRESS.= P 
ABSOL. TEMP.=T 
WEIGHT = Wj 



VOLUME = Va 
ABSOL. PRESS? Pi 
ABSOL. TEMP.=T 
WEIGHT = VV 



Fig. 2. 



The weight of two equal volumes of air, having the same 
absolute temperature, varies directly as the absolute pressures. 

W P 

yrr.Pi 

in which W = weight of a given volume of air at an absolute 
pressure P 
Wi = weight of an equal volume of air at an absolute 
pressure Pi 

23. Weight of 1 cu. ft. of Air at Atmospheric Pressure P at 
Sea Level and at any Absolute Temperature Ti. — According to 
Article 2, 1 cu. ft. of air at atmospheric pressure at sea level and 
at 60° Fahr. weighs 0.0764 lb.; hence the weight Wi of 1 cu. ft. 
of air at atmospheric pressure but at an absolute tempera- 
ture Tx is 

Wx T , TTr T 0.0764 (60+461) 39.804 
^jy=Y~ whence ^1 = ^^"="" f = — jT~ 

Thus, we find the weight of 1 cu. ft. of air at atmospheric pres- 
sure at sea level and at any absolute temperature T\ by dividing 
the constant 39.804 by the absolute temperature Ti. 



WEIGHT OF AIR 13 

24. Weight of 1 cu. ft. of Air at any Absolute Temperature Ti 

and any Absolute Pressure Pi. — We have as before : Wx = — ^ — 

1 1 

= weight of 1 cu. ft. of air at atmospheric pressure at sea level 
and at any absolute temperature 7\. 

If we now designate by W 2 the weight of 1 cu. ft. of air at the 
same absolute temperature Ti but at any absolute pressure Pi 
we have from Art 22: 

Wi atmospheric pressure at sea level 
W 2 = ~ Pi 

Wi 14.7 
W\~ Pi 

Substituting the value of W\ from Art. 23 we get J w = p 

whence W 2 = 2.7077 ^ (1) 

Thus, we find the weight of 1 cu. ft. of air at any absolute pres- 
sure and temperature by multiplying the absolute pressure in 
pounds per square inch by the constant 2.7077 and dividing the 
product by the absolute temperature. 

Example. — The weight of 1 cu. ft. of air at 60 lb. gage and at 100° 
Fahr. at sea level is: 

60+14.7 
1-00+461 

Table I gives the weight of 1 cu. ft. of air at various gage pressures and 
temperatures at sea level. 

24a. When using formula (1), Article 24 for computing the 
weight of 1 cu. ft. of air at an elevation above sea level, it must 
be borne in mind that Pi in that case is the gage pressure plus 
the atmospheric pressure at that elevation. 

Example. — What is the weight of 1 cu. ft. of air at 60 lb. gage and at 
100° Fahr., at an elevation of 8000 ft. above sea level? 

From Table VI, atmospheric pressure at an altitude of 8000 ft. above 
sea level is: 10.87 lb. per square inch; hence: 

PF 2 = 2.7077x|JJJJ 6 8 1 7 = 0.3421 lb. 



TF 2 = 2.7077 , nn \ ,;, =0.3602 lb. 



CHAPTER III 
THE COMPRESSION OF AIR IN AIR COMPRESSORS 

25. The Air Cylinder of a Compressor. — Fig. 3 shows the air 
cylinder (A) of a reciprocating compressor, in which the air is 
compressed by a piston (B), whose rod (C) is connected to the 
piston of a steam engine or through a connecting rod and crank to 
a revolving shaft, the latter being driven by some form of prime 
mover. 

The cylinder shown is that of a single-stage compressor, in 
which the air is compressed in one operation and in one cylinder, 
from initial to final pressure. In two- and multi-stage compress- 
ors the air is compressed gradually in succeeding cylinders, 
being cooled to in-take temperature while passing from one 
cylinder to the next one. (See Article 57.) 

26. Water-jackets. — As shown in Fig. 3, the cylinder heads 
and usually the main body of the air cylinders are water-jacketed. 
The chief object of this is to prevent the cylinders from reaching 
a temperature which would vaporize the lubricating oil and thus 
cause rapid wear of piston and cylinder. Incidentally the air itself 
is cooled to some extent by the surrounding water, which means 
a gain in efficiency. 

27. Inlet and Discharge Valves. — Modern compressors as a 
rule are double acting, that is, air is taken in, compressed, and 
discharged on the forward stroke as well as on the backward 
stroke of the piston. For this reason each of the cylinder heads 
carries one or more inlet valves a, a' through which the atmos- 
pheric air can enter the cylinder, and one or more discharge 
valves b, b' which open outward into closed ports g, h con- 
nected by a conduit c, which leads to a closed receiver R, whence 
the compressed air is conveyed to the place where it is proposed 
to use it. The inlet and discharge valves are either mechanically 
moved, resembling in their general form and operation the steam 
valves of a Corliss engine, or they are of the poppet type, being 
pressed upon their seats by a spring. In Fig. 3, which shows the 
section of the air cylinder of an air compressor, the inlet valves 

14 



COMPRESSION OF AIR IN AIR COMPRESSORS 



15 



a, a' are mechanically moved, the discharge valves b, b' are of the 
poppet type. For description of valves see Articles 144-153. 

28. Analysis of Single-stage Compression. — At the beginning 
of the stroke all valves are closed. The piston moving from right 
to left, as shown in the figure, causes a partial vacuum behind it; 



SAFETY VALVE 




PRESSURE GAUGE 



DISCHARGE VALVE 



WATERJACKETED CYLINDERH 




Fig. 3. — Diagram Illustrating Principle of Single-stage Compression. 



the inlet valves open under atmospheric pressure (unless opened 
mechanically) and the outside or free air rushes into the cylinder 
behind the receding piston. 

On the left-hand side of the piston we have at the beginning of 
the stroke a cylinder full of atmospheric or free air, which by 
the advancing piston is compressed into a steadily decreasing 
volume. The pressure of the air on this side of the piston is at 



16 COMPRESSED AIR 

the same time steadily increasing until at a certain point of the 
stroke it reaches, or slightly surpasses, the receiver pressure. 
Beyond this point the increasing pressure causes the discharge 
valves to open, and to the end of the stroke the compressed air is 
delivered into the receiver under constant pressure. 

If the inlet valves in the left-hand side of the cylinder are of the 
poppet type, they are kept closed during the forward stroke of the 
piston by the pressure of the air inside the cylinder, which is 
greater than the outside atmospheric pressure. 

29. The Receiver pressure depends on the work which the 
compressed air is to perform. If, for instance, the air engines 
at the end of the pipe line require a pressure of 80 lb. gage, no 
air is to be drawn from the pipe line until the gage of the receiver 
near the compressor shows this pressure, plus the pressure 
required for transmission. After this, the supply of compressed 
air must keep pace with the demand. Should the demand exceed 
the supply, the pressure of the air would-drop below 80 lb., thereby 
impairing the efficiency of the air engines. If on the other hand 
the supply at any time should exceed the demand, the pressure 
of the air in the receiver and in the pipe line would increase until it 
reaches the pressure for which the safety-valve of the receiver is 
set, when it will blow off through the latter. 

As this means a waste of energy, compressors which furnish 
air for intermittent work are generally supplied with automatic 
regulating devices, such as are described and illustrated in 
Articles 157-160. 



CHAPTER IV 

THEORY OF AIR COMPRESSION 

A. ISOTHERMAL COMPRESSION 

30. According to Boyle's Law, at constant temperature the 
volume occupied by a given weight of air varies inversely as the 
absolute pressure: 

vr-p 

v 

whence Pi =P^r 

V i 

in which V = the volume of a given weight of air at an absolute 
pressure P and a certain temperature. 
Vi = the volume of the same weight of air at the same 
temperature and at any absolute pressure Pi. 

Take, for instance, 1 cu. ft. of free air at 60° Fahr., having 
an absolute pressure of one atmosphere or 14.7 lb. per square 
inch. Assume that this air is confined under the piston of a 
closed cylinder, and that driving the piston forward we reduce 
the volume occupied by the air to 1/2 cu. ft., at the same time 
maintaining its temperature at 60° Fahr., then the absolute 

pressure of the air would be Pi = 14.7 Xtt = 29 A lb. per square 

Vs 
inch, or twice what it was before. 

If the volume were reduced to 1/3 cu. ft., its absolute pressure 
would become 3X14.7 = 44.1 lb. per square inch, or 29.4 lb. 
gage, always upon the condition that the temperature remains at 
60° Fahr. 

In other words, if the volume of air becomes 1/2, 1/3, 1/4, etc., 
times the original volume, its pressure becomes 2, 3, 4, etc., 
times the original pressure, always taking absolute pressures. 

31. Graphical Illustrations of Isothermal Compression. — Let 
Fig. 4 represent the air cylinder of a compressor, 48 in. long 
with a piston moving in it in the direction of the arrow. Let 

2 17 



18 



COMPRESSED AIR 



the cylinder be connected to a receiver in which the pressure 
is 73.5 lb. gage or six atmospheres per square inch. 

Assume that the cylinder has been filled with atmospheric 
air during the suction stroke of the piston. By moving the 
piston 12 in. from the left to the right, the volume of the air 
48 — 12 3 
■jx — = j of the original volume and the pressure 



is reduced to 



has increased to 4/3 times the atmospheric pressure, that is, to 
4/3X14.7=19.6 lb. absolute or 4.9 lb. gage. 



> p VOL. ^1 
d\ DELIVERY C 




^^^M^M^^^^^^^^^Z^^^^^^b 



STROKE =48 INCHES- 
AIR CYLINDER 



W///////////////////^^^^^^ 




TO RECEIVER 
AT 73.5 LBS. 



INLET 



Fig. 4. — Diagram Illustrating Isothermal Compression and Delivery. 



When the piston has advanced to a point 24 in. from its first 

48 — 24 1 
position, the volume of air has been compressed to . .„ — = « 

of the original volume and the pressure is now twice that of the 
atmosphere, that is ; 29.4 lb. absolute or 14.7 lb. gage. 

The same reasoning applies to other positions of the piston 
until the latter reaches a point 40 in. from the starting point. 

48 — 40 1 
The air has now been reduced to — jx — = « of the original volume 

and the pressure has increased to six atmospheres, that is, 88.2 






THEORY OF AIR COMPRESSION 19 

lb. absolute or 73.5 lb. gage. This being the pressure in the 
receiver, the discharge valves open and the remaining 8 in. of 
the stroke are completed by the piston against a constant pressure 
of 73.5 lb. in delivering the air into the receiver. 

32. Construction of the Isothermal Compression Curve. — Draw 
a horizontal line, AD, which at a convenient scale represents 
48 in. and mark on this line points at 12, 24, and 40 in. from its 
left end; then draw at those points lines perpendicular to AD. 

On these lines, measure off, at any other convenient scale, 
the gage pressures corresponding to the stroke; this will give a 
succession of points a, b, c, d, and, if we join them by a continuous 
line, we get a curve A-B which represents the variations of air 
pressure during the compression; that is, the gage pressure at 
any point M is measured by the line MN. 

The curve A B is sl hyperbola and is known as the curve of 
isothermal compression. Its equation is : 

PV = constant 

If we took any number of intermediate points between 40 and 
48 in. of the stroke, the pressure would always be 73.5 lb. gage, 
consequently a line drawn connecting these points will be a 
straight line parallel to AD. It represents the period of delivery 
under constant pressure. 

33. Work of Isothermal, Single-stage Compression and 
Delivery. — Work is the product of a force and the distance 
through which it acts in the direction of its application. 

In the diagram, Fig. 5, let AB represent an isothermal com- 
pression curve 

BC = the line of delivery 
Pi and P 2 = absolute initial and terminal pressures in pounds 
per square inch 
L = length of stroke in feet. 

The force acting on the body of air contained in the cylinder 
is the force applied to the piston by some external agent, such as 
steam, water, electricity, etc. The displacement of the point 
of application during one stroke of the piston is the length of the 
stroke (L). 

The force applied to the piston must be equal (theoretically) 
to the resistance offered by the air inside the cylinder, that is, to 



20 



COMPRESSED AIR 



its pressure, which at any point of the stroke is proportional to 
the volume into which the air has been compressed. 

During compression of the air from A to B the pressure in- 
creases from an absolute pressure Pi to an absolute pressure P 2 ; 
during the remainder of the stroke from B to C the air which now 
occupies a volume V 2 , represented by the distance BC, is de- 
livered into the receiver at a constant absolute pressure P 2 . 




Fig. 5. 



The average resistance of the air during the entire stroke is the 
mean pressure of the air against the piston. Its value in terms of 
absolute pressure in pounds per square inch is represented by a 
line EF, located somewhere between M and 0. 

Let A — area of piston in square feet 
L = length of stroke in feet 
Pi = absolute initial pressure of in-take air in pounds per 

square inch 
P 2 = absolute terminal pressure in pounds per square inch 
P e = mean absolute pressure in pounds per square inch 
W = total work performed per stroke in foot-pounds 
W n = net work performed per stroke in foot-pounds 
Vi = volume of free air in cubic feet taken into the cylinder 

per stroke 
Vi = volume of air in cubic feet after being compressed to an 
absolute pressure P2. 



. THEORY OF AIR COMPRESSION 21 

The total mean force acting on the piston during the entire 
stroke is 144 P e A lb. and the total work performed per stroke is 

TT = 144P c ^Lft.-lb. 
But AL = V 1 

hence W - 144P e Fi ft.-lb. (1) 

If in the diagram, Fig 5, we substitute for the length of the stroke 
(L) the volume Vi in cubic feet of free air, taken into the cylinder 
per stroke, then the product P e V\ in equation (1) is equal to the 
numerical value of the area MABCO. This value is obtained 
by multiplying P e , expressed in pounds per square inch, with V h 
expressed in cubic feet. 

The total work done during one stroke of the piston is as follows : 

Wi = work of compressing a volume Vi of free air from an 
absolute pressure Pi to an absolute pressure P2. This 
work is proportional to the area MABR. 

w z = work of delivering the compressed air which now occu- 
pies a volume V2 into the receiver under a constant 
absolute pressure P 2 . This work is proportional to the 
area BCOR. 

The sum of the two quantities wi and w 2 includes 

w 3 = work of filling the cylinder behind the advancing 
piston with a new volume of free air which is to be 
compressed during the return stroke of the piston. 
This work is proportional to the area MADO. 

The work w^, however, is not performed by energy supplied 
by the compressor, but by the pressure of the in-take (atmos- 
pheric) air. Measured in foot-pounds it is 

^ 3 = 144P 1 7i 

in which the product P\V\ is equal to the numerical value of 
the area MADO, 

34. The net work W n in foot-pounds performed by the com- 
pressor during one stroke of the piston is, therefore: 

W n = 144 X (area MABCO minus area MADO) 
= 144 X (shaded area ABCD) 



22 COMPRESSED AIR 

But area A£CD = area MABR 
plus area BCOR 
minus area A DOM 

AreailfAPP = I PdV 



•P 



Vi 
For isothermal compression PV=PiVi or P=Pi^- 



J ^ 






and since 



Vi 
—PiVi Naperian log yt 

V 2 

V 2 Pi 

p 

Area MABR=P 1 Vi Naperian log ^ 

* 1 

Area BCOR=P 2 V 2 

Area ADOM=P 1 V 1 

Therefore, JF„ = 144 (P^ Naperian log 3 ^+P 2 V 2 -P 1 V l ) 

■t i 

and since under isothermal conditions P 2 V2=PiVi. 

35. Net Work of Isothermal Compression and Delivery per 
Stroke : 

W n =lUP 1 V 1 loge^fi-lb. 

in which Pi = initial absolute pressure in pounds per square 
inch. 
P 2 = final absolute pressure in pounds per square inch. 
Vi — volume of free air in cubic feet taken into the 
cylinder per stroke. 
log e = Naperian log = 2.302585 times common log. 

36. Mean Gage — Pressure, Isothermal Compression and 
Delivery : 

Let P m = mean gage pressure in pounds per square inch. 
A = area of piston in square feet. 
L = length of stroke in feet. 



THEORY OF AIR COMPRESSION 23 

Vi = volume of air in cubic feet taken into the cylinder per 

stroke. 
W n = net work per stroke in foot-pounds. 

Then W n = 144 P m AL and since AL = Vi 

W n 



W n = 144 P m 7i whence P T 



144 Vi 



P 2 

or P m = Pi loge ^r lb. per square inch. 

Column 6 of Table III gives mean gage pressures for isothermal 
compression and delivery and for various terminal gage pressures. 

37. Theoretical Horse-power, Isothermal Single-stage Com- 
pression and Delivery. — The theoretical horse-power required to 
compress isothermally in one stage a volume Y\ of free air per 
minute from an absolute pressure P\ to an absolute pressure P 2 
and deliver the compressed air into the receiver under constant 
pressure is found from the general formula: 

PLAN 
Horse-power = 33^ 

in which P = mean gage pressure in pounds per square inch. 
L = length of stroke in feet. 
A = area of piston in square inches. 
N = number of strokes per minute. 

If we now let Vi designate the volume of free air in cubic feet 
taken into the cylinder per minute, we have: 

from which LAiy = 144Fi 

Substituting this value and the value P m for P in our formula, 

we get 

144 P 1 V 1 , P 2 
Horse-power = ^ Q0Q log,^ 

in which Vi = volume of free air in cubic feet taken into the 
cylinder per minute. 
Pi = initial absolute pressure in pounds per square inch. 
P 2 = terminal absolute pressure in pounds per square 

inch. 
log e = Naperian log = 2.302585 times common log. 



24 



COMPRESSED AIR 



Column 3 of Table V gives the theoretical horse-power required 
to compress 1 cu. ft. of free air per minute isothermally in one 
stage to various gage pressures and deliver it at that pressure 
into the receiver. 

38. Isothermal compression in actual practice is impossible of 
attainment. It is only approached in slow-speed compressors, 
where the air is in contact with the water-jackets for a longer 
time than in normal speed machines. 

In actual practice the compression curve as obtained from 
indicator diagrams falls closer to the adiabatic than to the 
isothermal curve. For this reason the formulas for adiabatic 
compression are generally used in practical compressor com- 
putations. 

39. Isothermal Expansion. — If compressed air could be ex- 
panded isothermally down to atmospheric pressure in an air 
engine, the theoretical work performed would be the same as 
the work required for isothermal compression and delivery. 
Hence, work of isothermal expansion : 



144 PxFi / P 2 
Horse-power = ^ m log, ^ 



(1) 



in which Pi = absolute pressure of exhaust air in pounds per 
square inch. 
= atmospheric pressure. 
Vi = volume in cubic feet per minute, which the volume 
V 2 of compressed air, admitted into the air engine 
per minute, would occupy after expansion to 
initial pressure. 
P 2 = absolute pressure in pounds per square inch of 
the air admitted into the air engine, 
loge = Naperian log = 2.302585 times common log. 

In expansion work we usually know the volume F 2 of com- 
pressed air taken into the cylinder of an air engine per unit of 
time, and since under isothermal conditions 

PlVl =p 2 v 2 

We can also write: 

Theoretical horse-power isothermal expansion: 

__ 144 P 2 7 2 , P 2 

Horse-power = 33 0QQ log e p- (2) 



THEORY OF AIR COMPRESSION 25 

in which P2 = absolute pressure of air taken into cylinder in 

pounds per square inch. 
Pi = exhaust (atmospheric) pressure. 
V2 = volume of compressed air in cubic feet taken into 

the cylinder per minute. 

At the present stage of the art, isothermal expansion is im- 
possible of attainment in actual practice. The formulas in- 
troduced under this article, however, are useful for comparison 
and for estimating efficiencies of compressores, pipe lines and air 
engines. 

B. ADIABATIC COMPRESSION OF AIR 

Theory 

40. We have seen that if air is compressed, heat is gene- 
rated. 

In adiabatic compression this heat is allowed to accumulate 
unchecked during the period of compression. As a consequence, 
when a certain pressure is reached, the corresponding volume of 
air will be greater on account of this heat than the volume which 
the air would occupy if the compression up to that same pressure 
had been isothermal. When the volume is reduced to one-half, 
the pressure is not only double as in isothermal compression, but 
more than double because of the heat, generated during compres- 
sion, being still in the air. 

Again, when the pressure has been doubled, the volume will 
not be one-half, but will be more than one-half, owing to the 
expansion due to heat which has remained in the air. 

Since the pressure rises faster than the volume diminishes, 

P . Vi 

p- is no longer equal to but is greater than y To form an 

Vi 
equation, the value of -y must be increased. This is done by 

Vi 
introducing an exponent 'V which raises the value of y to a 

power whose index has been found to be the ratio between the 
specific heat of air at constant pressure, and the specific heat 
at constant volume, expressed either in heat units (B.T.U.'s) or 
in foot-pounds. 

C P 0.2375 _K P 184.8 
n " C v ~ 0.1689 "Jr. 131.6 ' UD U; 



26 COMPRESSED AIR 

This gives for the general equation of the adiabatic compression 
or expansion curve: 

P V n =p 1 V 1 n (2) 

and, since the exponent n takes care of the changes in tempera- 
ture, due to adiabatic compression or expansion, we have from 
analogy with deductions made under Article 16: 



P7 B =Pi7i" = constant (3) 

K v 



The synthetical method by which ' V is found to equal 



is shown in Article 117a. 

The value of n varies slightly with the variation in the specific 
heats of air, due to the presence of moisture, as pointed out under 
Article 8. Throughout this treatise, the value 

n = 1.406 
will be used. 



RELATION BETWEEN TEMPERATURE, VOLUME AND 
PRESSURE IN ADIABATIC SINGLE STAGE COM- 
PRESSION OR EXPANSION OF AIR 

41. The relation between temperature, pressure, and volume 
of air at the beginning and at the end of adiabatic single stage 
compression or expansion can be deduced from Charles' and 
Boyle's Laws as follows: according to these laws (see Article 20, 
equation (3)). 

PiV 1 =PVp (1) 

whence P~ = V~f ^ 



For adiabatic compression 



P (Vi 
P 



\-m « 



Pi 

or -p 



/ V\ n VT 1 
combining equations (2) and (4) \rr) = y~^ 



THEORY OF AIR COMPRESSION 


27 


whence 


\7i/ " T 


(5) 


and 


Vi~\T) 




or 


Vx (T\h 

V " \TJ 


(6) 


from equation (3) 
or 


7i /P\» 
F /PAT 

Fi""\py 


(7) 


whence 


©"=©" 




n-l 

combining with equation (5) ^ = ij£) 


(8) 


and 




(9) 



This gives the following relations between volume, pressure, and 
temperature in adiabatic single stage compression or expansion : 
From (5) absolute temperature in terms of volumes 

r.-r(fj do) 

From (8) absolute temperature in terms of absolute pressures 

Tl=T Qy (id 

From (6) volume in terms of absolute temperatures 



28 COMPRESSED AIR 

From (7) volume in terms of absolute pressures 



From (9) absolute pressure in terms of absolute temperatures 



*-**) 



Ti\ n ' 1 (14) 



From (4) absolute pressure in terms of volumes 

p - p ©" (15) 

in which V = volume corresponding to an absolute pressure P 

and an absolute temperature T. 

Vi = volume corresponding to an absolute pressure 

Pi and an absolute temperature T\ and vice versa. 

n = exponent of adiabatic compression ( = 1.406). 



41a. Law of Thermodynamics, Applied to Adiabatic Com- 
pression and Expansion of Air. — According to the law quoted 
under Article 6 heat and work are mutually convertible. In 
adiabatic compression of air all the work of compression is 
converted into heat (see Article 117), and the temperature of the 
air is increased correspondingly. 

In compliance with the law referred to, a volume of com- 
pressed and therefore heated air, if allowed to expand adiabat- 
ically to initial pressure, against an external resistance, would 
perform work by converting back into mechanical energy all the 
heat received during compression. Theoretically, the amount of 
work performed will be equal to the work of compression. The 
temperature of the expanded air will be the same as before 
compression. 

In compressed-air installations, practically all of the com- 
pression heat is abstracted from the air by water-cooling and 
radiation, previous to expansion. In this case the compressed 
air is still capable of doing expansive work as before, by con- 
verting heat into mechanical energy. But the capacity for doing 
work will be less than in the first case, due to the loss of the 
compression heat which is equivalent to a loss of energy. 



THEORY OF AIR COMPRESSION 29 

It is obvious that in the second case the heat required to do 
work must come from some source other than the compression 
work. As a matter of fact, it is heat which was contained in 
the air before compression. That the expansive work consumes 
some of this heat is manifested by the cold created around the 
cylinders of an engine using air expansively. 

The actual temperatures of the compressed and of the ex- 
panded air under various conditions may be determined by 
applying the laws and formulas given in preceding articles. 

Example. — Let a volume 7=10 cu. ft. of free air be adiabatically 
compressed in one stage from atmospheric pressure (P = 14.71b. absolute) 
to 80 lb. gage (Pi = 94.7 lb. absolute); the initial temperature of the air 
being 60° Fahr. (^ = 521 degrees absolute). 

From equation (11), Article 41, we deduce the absolute temperature 
(Ti) of the air after adiabatic compression: 

7\ = T (*j\ ^ = 521 / 94 - 7 \ 029 = 894.25° absolute. 
1 \PJ \14.7/ =433.25° Fahr. 

The volume Vi into which the air has been compressed under adia- 
batic conditions, we find from equation (13), Article 41: 

If we cool this volume Vi of compressed and heated air to initial tem- 
perature of 60° Fahr. (T = 521 degrees absolute), the effect, according 
to Article 5, will be a decrease of pressure under constant volume. 
Calling the new pressure P 3 , we find same by applying the law stated 
under Article 19: 

Px T x 
whence P 3 =Pi jr = 94.7 -gf^= 55.174 lb. absolute. 

The volume of the cooled air has, of course, remained the same, viz. : 
2.664 cu. ft. 

If the air, occupying a volume V\ at an absolute pressure of 55.174 
lb. and a temperature of 60° Fahr., were allowed to expand adiabatic- 
ally down to atmospheric pressure, the temperature of the expanded 
air, according to equation (11), Article 41, would be: 




55.174 



\ 029 = 355.06 degrees absolute. 
7 = —105.94° Fahr. 



30 



COMPRESSED AIR 



and from equation (13), Article 41, the volume 7 2 of the expanded air 
would be: 

F a =7 1 (5) 4 = 2 .664(^) - 71 =6.8143eu.ft. 

This is the same quantity (weight) of atmospheric air we started out 
to compress, but, being so much colder (-105.94° Fahr.), occupies a 
smaller volume than the original volume of 10 cu. ft. If we now heat 
this cold exhaust air to initial temperature (60° Fahr.), under constant 
pressure, we should get our original volume. Applying the law stated 
under Article 18, we have: 

V 2 T 2 



whence 



V= V 2 tjt = 6.8143 

J- 2 



60+461 
355.06 



10.00 cu. ft. 



42. Graphical Illustration of Adiabatic Compression. — 

Assume a cylinder (Fig. 6) whose stroke is 48 in. and which 




-Hot oH>.459 oriq. vou-> 

II ^| gl rI 

■r^~"tf i-t -il-!- - 612 0RIG - V0L -^ 

)| o .1 ,| .1 



' 5 



I ATMOS. 



-! <J 

Y Y Y 



-TOTAL ORIGINAL VOLUME" 



^^/W/^^/W^^^ 




STROKED 48 INCHEST" 



■>! 



\w^^ ' 



SS^a^^jaa^^^^^^ 



AT 73.5 LB&. 



^» 



Fig. 6. — Diagram Illustrating Adiabatic Compression and Delivery. 



is filled with air at atmospheric pressure at a temperature of 
60° Fahr. and having a piston moving in it in the direction of 



THEORY OF AIR COMPRESSION 



31 



the arrow. Let the cylinder be connected with a receiver in 
which the pressure is six atmospheres or 73.5 lb. gage. 

If we move the piston from left to right and compress the 
air in the cylinder to two atmospheres, the volume will not be 
one-half the original volume (as in isothermal compression) but 
will be greater than one-half. 

From column 3 of Table IV we find that the volume is 0.612 
times the original volume, hence the piston will be at a point 
48- (0.612X48) = 18.63 in. from the left end of the cylinder. 
Thus we find the position of the piston at a pressure 

of 2 atmospheres to be at 48- (0.612X48) = 18.63 in. 
of 3 atmospheres to be at 48 - (0 . 459 X 48) = 25 . 97 in. 
of 4 atmospheres to be at 48- (0.374X48) =30.05 in. 
of 5 atmospheres to be at 48 -(0.319X48) =32.69 in. 
of 6 atmospheres to be at 48- (0.281X48) =34.51 in. 

from the left-hand end of the cylinder. 

43. Construction of the Adiabatic Compression Curve. — Draw 
a horizontal line AD which, at a convenient scale represents 48 
in., and mark on this line points at 18.63, 25.97, 30.05, 32.69, 
and 34.51 in. from the left end; then draw at those points lines 
perpendicular to AD. 

On these lines measure off, at any scale, the gage pressures 
corresponding to the stroke; this will give a succession of points 
a, b, c, d, e, f, and if we join these by a continuous line we get a 
curve A B which represents the variations of air pressure during 
compression, that is, the gage pressure at any point M is measured 
by the line MN. 

The curve AB is known as the curve of adiabatic compression. 

If we took any number of intermediate points between 34.51 
and 48 in. of the stroke, the pressure would always be 73.5 lb. 
gage, and consequently a line connecting these points will be a 
straight line BC parallel to AD. It represents the period of 
delivery under constant pressure. 



WORK OF ADIABATIC SINGLE-STAGE COMPRESSION AND 

DELIVERY 



44. The net work in foot-pounds performed during one com- 
plete stroke of the piston in compressing adiabatically a volume 
Vi of free air from an absolute pressure Pi to an absolute pressure 



32 



COMPRESSED AIR 



Pz and in delivering the compressed air which now occupies a 
volume V 2 , under constant pressure P 2 into the receiver, is 
obtained in the identical manner as has been shown for isothermal 
compression. 

Referring to Fig. 7, net work performed by the compressor un- 
der the conditions named is W n = 144 X (shaded area ABCD) ft. lb. 




AIR CYLINDER 



Fig. 7. 

But area ABCD = area MABR 
plus area BCOR 
minus area A DOM 



= Pd 



Area MABR = | PdV 
For adiabatic compression 

PV n =P 1 V 1 n or P=^f 



Hence 



area MABR = 



^ »-DELIVEBY 



w 






THEORY OF AIR COMPRESSION 
= P 1 V 1 n | t ,/T 



33 



L n ( V- 



-™p& 



P 1 V 1 n V 1 1 ~ n -P 1 V 1 n V 2 1 ~ n 



And since 

We can write area MABR = 



1— n 
PiV 1 n =P 2 V 2 n 

PiV 1 n V 1 1 - n -P 2 V 2 n V 2 1 ' n 



or, area MA BR = 



1-n 

P2V2-P1V1 
n-1 



Area BCOR=P 2 V 2 
Area ADOM=P 1 V 1 

P 2 V 2 -PiVi 

Therefore area ABCD= 2 / +P 2 F 2 -Pi7i 

n— 1 

_ P2F 2 -P 1 y 1 +nP 2 7 2 -nP 1 7i-P 2 7 2 +PiF 1 
n-1 

P 2 7 5 



t£i**<»H 



B-3-© 



Substituting we get 



Area^PCD = r ^P 1 7i[(^ ? ) " -l] and 

n-1 

45. Net work per stroke ^» = ~^ p i 7 i[(jr) " _1 ] ft -" lb - 

in which P x = initial absolute pressure in pounds per square 

inch. 

P 2 = final absolute pressure in pounds per square inch. 

Vi = volume of free air in cubic feet taken into the 

cylinder per stroke. 
n = exponent adiabatic compression (1.406) 
3 



34 COMPRESSED AIR 

46. Mean Gage Pressure, Adiabatic Single-stage Compres- 
sion and Delivery. — The mean gage pressure in pounds per 
square inch in single-stage adiabatic compression and delivery 
is deduced in the same manner as shown for isothermal com- 
pression. It is 

^™ 144 Vi or 



Pm = 



n- 



^Pi (W 5 ) —1 lb. per square inch. 



Column 7 of Table III gives the theoretical mean gage pressure 
in pounds per square inch for adiabatic single stage compression 
and delivery. 

47. Theoretical Horse -power, Adiabatic Single-stage Com- 
pression and Delivery. — The theoretical horse-power required 
to compress adiabatically a volume Vi of free air in one stage 
from an absolute pressure Pi to an absolute pressure P2 and to 
deliver the compressed air into the receiver at a constant pres- 
sure P2 is found from the general formula 

PLAN 
Horse-power = 33^ 

in which P = mean gage pressure in pounds per square inch. 

L = length of stroke in feet. 

A = area of piston in square inches. 

N = number of strokes per minute. 
If by Vi we designate the volume of free air in cubic feet taken 
into the cylinder per minute, we have 

whence LAN = 1447i. Substituting this value and the value 
P m for P in our formula we get 

__ 144 P^ n V(P*\^ ,1 m 

Horse-power = 33j()()()(7i _ 1) L( Fi ) -lj (1) 

in which Vi = volume of free air in cubic feet to be compressed 
and delivered per minute. 
Pi = initial absolute pressure in pounds per square 

inch. 
P 2 = terminal pressure in pounds per square inch. 
n = exponent of adiabatic compression (1.406) 



THEORY OF AIR COMPRESSION 35 

A glance at Fig. 7 shows that the work of adiabatic compression 
and delivery is greater than that of isothermal compression and 
delivery. In actual practice the indicator card from an air cylin- 
der of a compressor running at ordinary speed, shows a compres- 
sion line approaching the adiabatic curve much more closely than 
the isothermal; so closely that in making computations it is 
usually assumed that the compression has been adiabatic. 

Column 4 of Table V gives the theoretical horse-power required 
for adiabatic single-stage compression and delivery of 1 cu. ft. 
of free air per minute (Fi = 1.00) at sea level. 

48. Theoretical horse-power, single-stage adiabatic compres- 
sion and delivery, expressed in terms of absolute temperatures 
and weight of the volume of air to be compressed and delivered 
per minute: 

According to Article 20, equation (5) : 

PiF^OT! (1) 

in which Pi = absolute pressure of air in pounds per square foot. 
Vi = volume in cubic feet of 1 lb. of air at an absolute 
pressure Pi and an absolute temperature T\. 

From equation (7), Article 20, we have: 

R = (K P -K V ) = 184.8- 131.6 =53.2. 
From Article 40, equation (1), we have: 

K p 

jr 

whence K v = — 

n 

whence R = K V - K ^=~ -K p (2) 

n n 

From equation (9) in Article 41 we deduce: 

n 
P2 /Tz\ n ~ l 



2 =m 

'1 \tJ 



In substituting in the horse-power formula, Article 47, the value 
for P1V1 as given in equation (1) of this article, it must be remem- 
bered that in equation (1) the pressure Pi is expressed in pounds 
per square foot and the volume Vi is the volume in cubic feet of 
1 lb. of free air, whereas in the horse-power formula, Article 47, 



36 COMPRESSED AIR 

Pi is expressed in pounds per square inch and V\ is the volume 
of free air in cubic feet to be compressed per minute. Therefore 
if we wish to compress adiabatically and deliver w pounds of free 
air per minute, the formula becomes 

n n— 1 

Horse-power = w n ATl [ (Tl\ ^ ~*~ _ x ] 

(n-l)33,000L\Zy X J 

Introducing value of R from (2) 

„ n{n-\)K p T x [T 2 -T 1 l 

Horse-power = %(n _ ^ _ |__j 

Introducing the value for K p = 184 . 8 we get 

Theoretical horse-power = 0.0056 w[T 2 - Ti] (3) 

in which w = weight of the number of cubic feet of free air which 
are to be compressed and delivered per minute. 
T 2 = final absolute temperature of compressed air. 
T\ = initial, absolute temperature of free air. 

Example. — Find theoretical horse-power required at sea level to com- 
press and deliver 100 cu. ft. of free air per minute, having an initial 
temperature of 60° Fahr., the final pressure to be 85 lb. gage. 

From Article 23 we find the weight of 100 cu. ft. of atmospheric air 
at 60° Fahr. 

-"OSS-*"*. 

From equation (11), Article 41, we find the absolute temperature of 
the air after compression: 

n-l 



T 2 =T 1 

= (60+461) (^±l^)°' 29 = 908 o . 
7*! = (60+461) = 521° 

^-^ = 387° 
Theoretical horse-power = 0.0056 X7.64 X387 = 16.55 



THEORY OF AIR COMPRESSION 37 

RELATION BETWEEN FINAL PRESSURE OF A GIVEN QUANTITY 
OF AIR AND THE POWER REQUIRED TO COMPRESS TO THAT 

PRESSURE 

49. The formulas for the horse-power required to compress 
and deliver a certain volume of free air, show that this power 
is not directly proportional to the final pressure. For in the 

n— 1 

quotient (-5- ) the pressures are absolute pressures, that is, 

gage plus atmospheric pressures. 

Doubling the gage pressure would not double the expression 
p 

p- and therefore would not double the horse-power required to 

produce that pressure in the air. To illustrate: For a final gage 
pressure of 80 lb. 

The quotient p- is — 14.7 =6.442 

forl601b . g is l^+iil =11 . 88 

for 240 lb. y is 24 °* * 47 = 17.33 

Referring to column 7 of Table V, to compress 100 cu. ft. of 
free air per minute in two stages to 60 lb. gage requires 12.10 
h.p. (theoretically). To compress to 180 lb., which is three times 
as much, only requires 20.8 h.p. which is less than twice the horse- 
power required for compression to 60 lb. 

This points to conditions pertaining to compressed air which 
are advantageous in the transmission and final use in air engines 
as pointed out under Article 103. 

60. Modified Power Values for Practical Air Compression 
Problems. — In the preceding theoretical formulas no allowance 
has been made for clearance, the heating of the intake air in 
passing through the valves, and the friction of the compressor. 

The effect of the first two items on the consumption of power 
is negligible in good compressors. The additional energy required 
to overcome frictional resistance will amount in well-designed 
compressors to from 7 to 15 per cent, of the theoretical horse- 
power, depending to a great extent on the care that is taken 
with the machine. 

For practical compressor computations an addition of 15 per 
cent, is usually made to the horse-power derived from the theo- 
retical formulas. 



CHAPTER V 

CLEARANCE, VOLUMETRIC -EFFICIENCY, CAPACITY, SPEED, 
MECHANICAL-EFFICIENCY OF COMPRESSORS 

51. Clearance. — This is the space enclosed between the piston 
and the cylinder head at the end of the stroke. See Fig. 3. 

The clearance space, though generally a source of loss, is 
necessary for practical reasons: first, to avoid danger to the 
cylinder heads by allowing space for the water that may accumu- 
late in the cylinders, and second, to provide passage sufficiently 
large for ready admission and delivery of the air. 

It is evident that the clearance volume depends upon the area 
of the piston. In short-stroke cylinders of large diameter the 
clearance volume is a large proportion of the Piston Displacement 
The latter is the actual volume swept through by the piston in 
one stroke. 

Clearance is usually expressed as a ratio between clearance 
volume and cylinder volume. For cylinders of same diameter 
but different length of stroke, the ratio is larger in the short- 
stroke cylinder. In large, up-to-date compressors it varies from 
1 to 2 per cent. It is much more in very small, short-stroke 
machines. 

If the volume swept through by the piston in one stroke is 
1000 cu. in. and the clearance volume is 20 cu. in. the compressor 
has 2 per cent, clearance. 

52. Losses Due to Clearance. — If the discharge pressure is 
75 lb. gage or 89.7 lb. absolute and the initial pressure is atmos- 
pheric pressure at sea level, that is, 14.7 lb. absolute, the air re- 
maining in the 20 cu. in. clearance space will expand on the 
return stroke of the piston to about six times the clearance 
volume, or to 120 cu. in. and will, therefore, take up an addi- 
tional 100 cu. in. from the in-take cylinder. That is, in a 
cylinder of 1000 cu. in. piston displacement the piston must 
travel back 10 per cent, of the return stroke before the clearance 
air has expanded to atmospheric pressure and before the atmos- 
pheric air is allowed to flow into the cylinder. 

38 



MECHANICAL-EFFICIENCY OF COMPRESSORS 39 

The actual room for the admission of new free air is therefore 
only 1000-100 = 900 cu. in., or, as commonly stated, the volu- 
metric efficiency of the compressor is 90 per cent. 

Theoretically, the clearance loss, so called, is one of volumetric 
efficiency only and not of power. For although this air re- 
quired work in compressing it to receiver pressure, in expanding 
it helps to compress the air on the other side of the piston. 
The loss of power due to loss of heat during expansion of the 
clearance air usually is a negligible quantity. 

In practice, a loss of power is caused by clearance, due to the 
fact that, in order to deliver a definite amount of air, a larger 
compressor, consuming more power, is required. 

The loss of volumetric efficiency due to clearance is less for 
two-stage than for single-stage compression, because for any 
given capacity the low-pressure cylinder of the two-stage machine 
is practically of the same size and has the same percentage of 
clearance as the cylinder of a single-stage machine. But the 
terminal pressure in the low-pressure cylinder of the two-stage 
machine is much lower, hence the expansion of the clearance 
air back into the cylinder volume is much less, and as a conse- 
quence the volumetric efficiency is higher. (See Chapter VI 
on Compound Compression.) 

53. The volumetric efficiency of a compressor is the ratio of 
the volume of free air actually admitted and compressed in the 
in-take cylinder to the piston displacement. 

The diagram in Fig. 8 represents an ideal air card, in which 

GA is the admission line. 
AB is the compression line. 
BC is the delivery line. 
CG is the expansion line. 

This diagram shows graphically the loss in volumetric efficiency 
due to clearance and also that due to imperfections in the admis- 
sion of free air. In order to cause the outside air to flow into the 
cylinder, the pressure in the latter must be less than the atmos- 
pheric pressure; the admission line will therefore always fall 
more or less below the atmospheric line as shown exaggerated on 
the diagram. If the in-take areas are restricted, the drop in 
pressure may become considerable. The clearance volume is 
represented by the lines EF = CD. 



40 



COMPRESSED AIR 



FG is the extra volume occupied by the clearance air after 
expansion and if there were no other losses, the volumetric 
efficiency would be represented by the line AG. But on the 
forward stroke the piston must travel a distance AR before the 
atmospheric line is reached and before actual compression 
begins. Hence the actual volumetric efficiency in the case 
illustrated by the diagram is represented by the line RG. 




Fig. 8. — Air Card of a Single-stage Compressor. 



High-class large compressors have a volumetric efficiency of 
over 90 per cent. In small single-stage compressors with 
insufficient water cooling, restricted inlet areas, and leaking 
pistons, the volumetric efficiency will be found much below the 
above figure. 

It will be observed from the above that, in making calculations 
for a compressor plant to furnish a certain amount of free air 
per minute, it is quite important to make due allowance for 
volumetric efficiency. In installing a compressor plant, it is a 
wise precaution to have the builder guarantee a definite minimum 
volumetric efficiency. 

54. Capacity. — Compressor builders frequently call the free- 
air capacity of their machines the volume swept through by the 
piston, without making any deductions, that is, if the area of 
the piston is 2 sq. ft. and the latter travels 500 ft. per minute, 
the capacity is called 1000 cu. ft. per minute. 

Now, we have seen that if the clearance of a compressor, 
compressing to 75 lb. gage, is 2 per cent, the actual capacity is 
only 900 cu. ft. per minute and if 1000 cu. ft. capacity is wanted of 
the same compressor it must be speeded up to 555 ft. per minute. 



SPEED OF COMPRESSORS 41 

Clearance is one of the factors affecting capacity. Since the 
volume which the expanded clearance air occupies, increases as 
the pressure increases, it follows that the loss in capacity by 
clearance is directly proportional to the pressure. 

Another factor affecting compressor capacity is the condition 
of the air taken into the cylinder, which in common practice of 
rating capacities is assumed to be at atmospheric pressure and 
at no higher temperature than the outside source of supply. 
Such ideal conditions never exist. Even with unobstructed 
inlet passages air will not flow into the cylinder without some 
difference in pressure to force it in; hence the air taken into the 
cylinder always has a pressure slightly below that of the outside 
air. Then again, the entering air, coming in contact with the 
cylinder walls which have been highly heated during the com- 
pression in the preceding stroke, is heated to a temperature 
higher than outside temperature, thereby decreasing in density. 
As a consequence, at each stroke the compressor takes in a volume 
of air which weighs less than the same volume would weigh 
had it remained at outside temperature and pressure. 

The temperature of a given volume of air does not affect 
the power required to compress and deliver that volume, it 
merely expands or contracts the product. 

Table VII shows the effect of initial in-take temperature upon 
the efficiency and capacity of a compressor. 

55. Speed of Compressors. — From what has been said concern- 
ing the capacity of a compressor, it might be assumed that this 
capacity could be indefinitely increased by increasing the piston 
speed. This is true to a certain degree. The question is, where 
is the limit? The only general answer that can be given is, 
when it does no longer pay, in dollars and cents. 

Since the cost of compressing air must depend to a large ex- 
tent on industrial conditions, the price of labor, fuel, supplies, 
etc., in the locality where the air is to be used, the ultimate speed 
of an air compressor is usually the result of a compromise between 
first cost, operating cost, and efficiency. 

There are other factors which make speeds beyond a certain 
limit objectionable. It has been shown that in order to cause the 
air to flow into the in-take cylinder, there must be a difference 
between the pressures inside and outside of the cylinder. The 
outside pressure being normal atmospheric pressure, the pressure 
within the cylinder on the in-take-stroke must, therefore, always 



42 COMPRESSED AIR 

be something less than this. Increased piston speed demands 
an increase of velocity at which the air must flow into the cylinder, 
and this in its turn demands a greater difference between the in- 
side and outside pressure, that is, a reduced pressure in the in- 
take cylinder. 

From the diagram in Fig. 8 it will be seen that a large drop in 
pressure of the in-take air below atmospheric pressure means a 
lengthening of the distance AR, hence a decrease of volumetric 
efficiency. 

In following up this reasoning it becomes evident that a large 
increase of speed will usually give but a small increase in delivery, 
besides causing a rapid wear and frequent breakage of the work- 
ing parts of the machine, to say nothing of the increased fric- 
tion which in its turn reduces the mechanical efficiency of the 
compressor. 

Increased speed, furthermore, means increase in temperature 
because the air is rushed through the cylinder at a greater velocity 
and does not come in contact with the water-j ackets long enough 
to be cooled to any great extent. This rise of temperature in- 
creases the difficulty of lubrication and, if carried far enough, 
it may reach the ignition point of combustible substances in the 
cylinders, causing an explosion with all the expensive delays and 
repairs incident thereto. 

The catalogues of compressor builders show piston speeds of 
compressors all the way from 150 ft. per minute for small, single- 
stage, 6-in. stroke machines with a rated capacity of 30 cu.ft. 
of free air per minute, to 650 ft. per minute for a large, 5-ft. 
stroke, two-stage compressor, driven by a compound Corliss 
engine with a rated capacity of 8000 cu. ft. of free air per 
minute. 

56. The mechanical efficiency of a compressor is the ratio of 
the power theoretically required to compress and deliver a given 
quantity of air per unit of time to the power actually consumed. 

The power in excess of the theoretical power is chiefly re- 
quired to overcome frictional resistances of the machine, for 
which no return is made in the ultimate use of the compressed 
air. It therefore is a loss which can be minimized but not avoided 
altogether. 

The amount of friction is dependent both on the design of 
the compressor and on the care bestowed upon it while in 
operation. 



CHAPTER VI 

TWO-STAGE AND MULTI-STAGE COMPRESSION, ALSO 
KNOWN AS COMPOUND COMPRESSION 

THEORY 

67. Single-stage, isothermal and adiabatic compression of air 
from to 120 lb. gage is represented in Fig. 9 by the curves AC 
and AE respectively. 

In preceding articles it was explained that the work per- 
formed during one stroke of the piston is represented by the 
area in the diagram to the right of the compression curve. 
It was also explained that the expenditure of energy in adiabatic 
compression and delivery is greater than in isothermal compres- 
sion and delivery, on account of the increase in volume, due to 
the unchecked rise in temperature. 

In the diagram, Fig. 9, the area A DEC B A therefore stands 
for the waste of energy in adiabatic, single-stage compression 
and delivery, in which the heat of compression is allowed to 
remain in the air. This heat of compression represents work 
done upon the air for which there is no return, since during 
transmission the heat is all lost by radiation before the air is 
used. 

The problem of economy, obviously, becomes one of abstract- 
ing the heat generated in the air during the process of 
compression. As has been pointed out, this is partially ac- 
complished by water-jacketing of the cylinder walls. But 
owing to the short interval within which the compression 
takes place and the comparatively small volume of air actu- 
ally in contact with the cylinder walls, very little cooling of 
the air occurs. Cylinder jackets are, however, indispensable 
in keeping the cylinder walls sufficiently cool for effective 
lubrication, and in the prevention of cumulative heating, which 
in extreme cases may result in explosion. 

The impossibility of proper cooling within a single cylinder 
leads to the alternative of discharging the air from one cylinder, 
after partial compression has been effected, into a so-called 

43 



44 



COMPRESSED AIR 



inter-cooler, removing the heat generated during the first com- 
pression, and then compressing the air to final pressure in another 
cylinder. This method of accomplishing compression in two 
steps with intermediate cooling is called two-stage compression, 
or when repeated one or more times for high pressures, multi- 
stage compression. See Figs. 24 to 33 for designs of modern 
two- and multi-stage compressors. 

Referring again to diagram Fig. 9 and assuming the com- 
pression in each cylinder to be adiabatic, the compression 
curve is represented by the interrupted line ADBH; the compres- 



EHC 




Fig. 9. — Diagram Illustrating Two-stage Compression. 



sion proceeds adiabatically in the first or low-pressure cylinder 
to D; the air is then withdrawn and cooled under practically 
constant pressure in a suitable vessel called an inter-cooler, until 
its initial temperature is reached and its volume is reduced 
from ID to IB; with good inter-cooler arrangement it may be 
even further reduced; it is then introduced into a second or 
high-pressure cylinder and compressed adiabatically as before 
along the line BH to the final pressure. 

As before noted, the energy required in single-stage com- 
pression and discharge of a given quantity of air under isothermal 
conditions is proportional to the shaded area ABCFG. The 
additional energy required in two-stage adiabatic compression 
is proportional to the other shaded areas ADB and BCH; while 
the loss of energy in adiabatic single-stage compression and 
delivery compared with isothermal compression and delivery is 



TWO-STAGE AND MULTI-STAGE COMPRESSION 



45 



proportional to the whole area ADECBA. The saving effected 
by two-stage adiabatic compression and delivery is therefore 
represented by the unshaded portion DEHB. 

From Table V it appears that to compress 1 cu. ft. of free air 
per minute to 100 lb. gage and deliver it at that pressure into the 
receiver, requires 0.182 h.p. in single-stage and 0.158 h.p. in 
two-stage compression at sea level, showing a saving in energy of 
13 per cent, in two-stage compression. 

58. Analysis of Two-stage Compression. — Fig. 10 shows the 
low- and high-pressure air cylinders and the inter-cooler of 



-■■Intercooler, C 



Free Air. 

Air Compressed to 
Infercookr Pressure 

Air Compressed -to 

Receiver Pressure 




Discharge to 
Receiver at 
120 Lb. Qage. 

Free Air 
Intake 

Fig. 10. — Diagram Illustrating Principle of Two-stage Compression. 



an Ingersoll-Rand straight line steam-driven, two-stage air 
compressor. 

In order to study the principle of operation of this compressor 
we must assume that it has been running long enough to bring 
about normal working conditions; viz., that the pressure in the 
receiver has reached a required terminal pressure of, say, 120 lb. 
gage and that the inter-cooler is therefore filled with air at about 
30 lb. gage. 

To follow the air through its various stages from the in-take 
to the discharge during one stroke of the piston, let it be assumed 
that the pistons advance from right to left as indicated by the 
arrow in Fig. 10. During the previous stroke from left to right 



46 COMPRESSED AIR 

the inter-cooler (C) and its connections (F and G) to the air 
cylinders have been replenished with air compressed to 30 lb. 
This body of air is now shut off from both cylinders by their rela- 
tive valves and is losing the greater part of its heat and some 
of its pressure through the influence of the circulating cold water 
in the inter-cooler. The loss of pressure is quickly made up by 
the equalizing process explained below. 

During the first part of the return stroke from right to left 
the piston (L) in the low-pressure cylinder (A) acts only on the 
free air taken in on the previous stroke, while the high-pressure 
piston (D) is engaged in compressing to the terminal pressure the 
air in front of it, which has been admitted on the previous stroke 
from the inter-cooler at a pressure slightly under 30 lb. 

While the free air in the low-pressure cylinder '(A ) is being com- 
pressed, the advance of the piston (D) in the high-pressure 
cylinder reduces the pressure behind it, causing the high-pressure 
inlet valves (E) to open. The compressed air in the inter-cooler 
(C) and in the connections (F and G) now rushes into the high- 
pressure cylinder (B) thereby slightly expanding in volume and 
decreasing in pressure until the pistons have reached a point 
somewhat beyond midstroke. 

When the pistons have passed this point, the air pressure in 
front of the low-pressure piston (L) rises slightly higher than that 
in the inter-cooler, causing the low-pressure delivery valves (M) 
to open. From now on to the end of the stroke both cylinders 
are in communication with each other through the inter-cooler. 

The low-pressure piston now acts upon the entire body of air 
contained in the low-pressure cylinder, in front of the piston, 
in the inter-cooler, in the connecting passages and in the portion 
of the high-pressure cylinder behind the high-pressure piston. 
At the same time the air in front of the high-pressure piston 
is delivered into the receiver at constant final pressure. 

During this period an approximate equalization of pressure is 
established throughout. These fluctuations in pressure and the 
final equalization of pressure which take place during each stroke 
of the piston may be observed by watching the movements of 
the hand on the pressure gage (P) and from the indicator diagrams 
taken from compressors in normal operation. (See Chapter VIII.) 

Referring to the diagram, Fig. 9, the saving of energy in two- 
stage compression was explained as being due to the inter-cooler 
which reduces the volume ID of the compressed air, coming 



TWO-STAGE AND MULTI-STAGE COMPRESSION 



47 



from the low-pressure cylinder, to a volume IB, before admitting 
it into the second or high-pressure cylinder. 

In the above analysis of operation no mention is made of a 
reduction in volume. The reason for this becomes clear when it 
is realized that the air which enters the high-pressure cylinder 
from the inter-cooler is not the identical volume of air which 
leaves the low-pressure cylinder at that moment, but is a quantity 
of air that had been in the inter-cooler long enough to cool down 
to atmospheric temperature and, being cooled, occupies in the 
inter-cooler a smaller volume than it did when it entered it. The 
room made by the shrinkage is immediately filled at the other 
end of the inter-cooler by a quantity of hot air rushing into it 
from the low-pressure cylinder during the process of equalization 
mentioned above. 

The above description of the mode of operation does not 
strictly apply to a duplex cross-compound compressor such as 
shown in Fig. 28 because there the pistons work with one crank 
90 degrees in advance of the other, and at certain periods in the 
cycle of operation travel in opposite directions. The effect of 
the inter-cooler, however, is practically the same as in straight 
line machines. 

RATIO OF COMPRESSION IN COMPOUND OR MULTI-STAGE 
COMPRESSION 



59. The ratio of compression in any cylinder of a compressor is : 
terminal absolute pressure in that cylinder 



r = 



initial absolute pressure in that cylinder 






V B 

¥4 CO 

1 


1 


* 


© 



p 8 p. 



p* 



Fig. 11. 



The cylinders of a multi-stage compressor are dimensioned 
so that the work done per stroke in each cylinder is as nearly as 



48 COMPRESSED AIR 

possible the same, thereby equalizing and minimizing the strains 
on the machine. 

Let 1, 2, 3, 4 in Fig. 11 represent the cylinders of a multi-stage 
compressor, and let 

P a = initial absolute pressure in cylinder (1) in pounds per square 

inch, 
Pi = final absolute pressure in cylinder (1) in pounds per square 
inch, 
= initial absolute pressure in cylinder (2) in pounds per square 
inch, 
P 2 = final absolute pressure in cylinder (2) in pounds per square 
inch, 
= initial absolute pressure in cylinder (3) in pounds per square 
inch, 

&c. 
V a — piston displacement in cylinder (1) in cubic feet, 
V 2 = piston displacement in cylinder (2) in cubic feet, 

&c. 
then the net work per stroke of adiabatic compression and de- 
livery in cylinder (1) is, according to Article 45: 



n-l 



^n ,== ^I P « F «[(P) n _1 ] f00t -P° UIldS - (^ 

The net work per stroke in cylinder (2) is: 

n-l 

Tr .'--£lT J W(?;) " - 1 ] foot-pounds. (2) 

In compound compression the air between stages is supposed 
to be cooled to initial temperature under constant pressure; 
hence the volume F 2 of air, entering cylinder (2) from the inter- 
cooler at an absolute pressure Pi is the volume which cylinder 
(1) would deliver per stroke, had it compressed the in-take 
air V a isothermally during that stroke instead of adiabatically 
to the pressure Pi. From this it follows that in stage compres- 
sion with perfect inter-cooling between stages, Boyle's law 
(Article 15) becomes applicable: 



TWO-STAGE AND MULTI-STAGE COMPRESSION 49 

Substituting this value in equation (2) we get 
Net work per stroke in cylinder 2 : 

n— 1 

^/ = ^ Po7 «[(£~) " _1 ] foot -P° unds (3) 

Net work per stroke in cylinder 1 : 

n-l 

A glance at equations (3) and (1) shows that W " becomes 

p 
equal to W n ' when the ratio of compression -p- in cylinder (2) 

p 
becomes equal to the ratio of compression p- in cylinder (1). 

-to 

This leads to the general conclusion: In order that the work 
per stroke in each cylinder of a compound compressor be theo- 
retically the same, the following relations between the terminal 
and initial pressures in the various cylinders must exist: 





Px P 2 P 3 P 4 

Pa Pi P 2 P 3 


60. For two- 


stage compression we have : 




Pi P 2 




P a ~Pi 


Dividing by P a 


Pi 2 P 2 

Pa 2 " Pa 


Whence 


Pa Pi VP« 



(1) 



(2) 

This shows that the ratio of compression in each of the two 
cylinders must be equal to the square root of the total ratio of 
compression; the total ratio being the ratio between the final 
pressure in cylinder (2) and the initial pressure in cylinder (1). 

From equation (2) we get : 



\/p!~V 



Pi = P-\ir-\PJ , t (3) 



50 



COMPRESSED AIR 



61. For three-stage compression we have 

Pl_P 2 _P3 

P a Pi P 2 

Whence 



(i) 






Substituting this value in (1) 

Pi PsPc 
Pa Pi 2 



Dividing by P 



Whence 



Pa 3 Pc 

Pl_P2_P3 
Pa"Pl"P 2 " 



(2) 



That is, the ratio of compression in each of the three cylinders 
must be equal to the cube root of the total ratio of compression. 
From equation (2) we get 



Pi=pJ/^ 3 =^Pa 2 P< 

\* a 



-»$- 



VP a *Ps X \l^ = VPJPf 



62. For four-stage compression we would find 
Pi_P2_P3_P4_ aIPa 

Pa Pi P 2 P 3 \Pa 

Pl=Pa^ = ^IVP* 
\x a 

P 3 =P 2 ^ 4 -VPJP? X^g 'VPS? 



whence 



(3) 
(4) 

(1) 

(2) 
(3) 
(4) 



CYLINDER DIAMETERS OF MULTI-STAGE COMPRESSORS 



63. The cylinders of a multi-stage compressor are proportioned 
in accordance with the initial volume V a of free air to be com- 



TWO-STAGE AND MULTI-STAGE COMPRESSION 51 

pressed per stroke or per minute and the ratio of compression in 
each cylinder, as obtained from the formulas in Articles 60, 
61 and 62. 

In compressed-air computations the volume V a to be com- 
pressed per stroke or per minute is usually given; the length of 
the stroke is made the same in all cylinders; the number of 
strokes per minute is chosen with reference to the type of com- 
pressor desired and the number of cubic feet of air required per 
minute. 

Referring to Fig. 11 : 

Let V a = volume of free air in cubic feet, taken into cylinder (1) 
per stroke, 
V 2 = volume which the air discharged from cylinder (1) 
occupies at a pressure Pi after being cooled to initial 
temperature, 
= piston displacement of cylinder (2), 
V s = volume which the air discharged from cylinder (2) 
occupies at a pressure P 2 after being cooled to initial 
temperature, 
= piston displacement of cylinder (3), 
&c. 
di = diameter of cylinder (1) in inches, 
d 2 = diameter of cylinder (2) in inches, 

&c. 
A = area of piston in cylinder (1) in square inches, 
L = length of stroke in inches, 

then Fa ~144 X 12~ 1728 



whence di = 47 A /-=? inches. 



-W- 



Having thus determined the diameter di of the in-take or 
low-pressure cylinder (1), the diameters of the other cylinders are 
found as follows: 

The length of stroke being the same for each cylinder, the 
volumes of the cylinders are in the ratio of the squares of their 
diameters. Assuming complete inter-cooling between stages, 
the volumes according to Article 16, are also in the inverse 1 ratio 
of the pressures. In this connection it must be remembered 



52 COMPRESSED AIR 

that volume V2, for instance, is the volume which the air discharged 
from cylinder (1) would occupy after being cooled to initial 
temperature under constant pressure Pi. 
Referring to Fig. 11 we would have 



d 2 * 
dS" 


v 2 

Va 


Pa 
Pi 


1 

"Pi 

Pa 



hence 

square of diam. of one cylinder 1 _ 1 

square of diam. of preceding cyl. "ratio of compr. in each cyl. ~ r 

From Articles 60 to 62 we have: 

For two-stage compression: 



r /PAf \Pj 



For three-stage compression: 






For four-stage compression: 



r /P 4 \i \Pj 



Therefore : 



Cylinder Diameters 



64. Cylinder Diameters for a Two-stage Compressor. — 

d 1= 47J^- inches 

d» 2 (P \ * (P \ * 

^ = /-M whence d 2 = di(-~) inches 



TWO-STAGE AND MULTISTAGE COMPRESSION 53 

65. Cylinder Diameters for a Three-stage Compressor. — 

d 1 = 47J~ inches 
-A= (p^) whence d 2 = di(^-\ inches 

d? = {pj 0Td *= d2 \p;) 

11 i 

/p a \ 6 /p a \ 6 /p \ 3 

^3 = ^i(p^) X ( p^ ) whence d 3 = <M— M inches 

66. Cylinder Diameters for a Four-stage Compressor. — 

di = ^7yl-~ inches 

;A = (p7 whence d 2 = di(^-\ inches 

d 3 2 /P«\* , , /Pa\* 

ii i 

iP \ 8 /P \ 8 /P \ * 

^3 = <ii(p^j X ( p^) whence d 3 = di(pM inches 

d 4 2 /P«\* , , /P«\* 

5?=(k) OT *"*(/>;) 

^4 = ^i(p a ) x(p-) whence rf 4 = ^i(p^-) inches 

67. The volumetric efficiency of the compressor only affects 
cylinder (1). Therefore in the above calculations of the diam- 
eters di, d 2 , d s , etc., the value di as given in the formula will 
be used, and the final value of di will be di as found by the formula, 
plus an allowance, depending on the volumetric efficiency 
of the compressor. 

Example a. — What should be the diameters of the air-cylinders of a 
three-stage compressor to furnish 300 cu. ft. of free air per minute, 
compressed to 300 lb. gage? 



54 COMPRESSED AIR 

Length of stroke L— 16 in. 
Number of r.p.m. = 135 
Volumetric efficiency = 85 per cent. 
Diameter of piston rod = 2 1/2 in. 

b. What is the terminal pressure in each of the cylinders and what 
is the ratio of compression in each cylinder? 

Solution a. The number of revolutions being 135, the number of 
strokes per minute is 270. Hence the volume of free air taken into the 
cylinder per stroke is : 

270=1.11 cu. ft. 

To which must be added, volume of piston rod" 

16X2.5 2 X0. 7854 

■ 1728 = 0-045 cu. ft. 

Hence V a = 1.11+0.045 = 1.155 cu. ft. 



And d 1 =47\/l^ =12.63 in. 
\ 16 

/ 14 7 \ * 
d > ~ d ' \ 300+ 14. 7 ) =758in - 

/ 14 7 \ J 
ds = ( M 300+14.7 / =4 - 55in - 

The" diameter d x of the in-take cylinder must be increased to allow for 
a volumetric efficiency of 85 per cent. 

Calling the final diameter of the in-take cylinder x we have : 

x 2 100 
di>~ 85 

Whence x = d 1 J 1 ^= 12.63Xl.085 =13.71 in. 

^ 85 

Solution b. From Article 61, terminal pressure in 



Cylinder (1) Pi = x /14.7 2 X314.7= 40.81 lb. absolute. 

= 26.11 lb. gage. 

Cylinder (2) P 2 = ^/14.7X314.7 2 = 1 13.34 lb. absolute. 

= 98.64 lb. gage. 

Cylinder (3) P 3 =314.7 lb. absolute 

= 300.00 lb. gage. 



TWO-STAGE AND MULTI-STAGE COMPRESSION 
Ratio of compression in each cylinder: 



= 2.78 
= 2.78 
= 2.78 



55 





*Pa 


■* 


300+14.7 
14.7 


In cylinder (1) 






40.81 
14.7 


In cylinder (2) 






113.34 
40.81 


In cylinder (3) 






314.7 



THEORETICAL HORSE-POWER, COMPOUND COMPRESSION AND 

DELIVERY 

68. For two-stage compression, the theoretical horse-power 
required to compress adiabatically a volume of free air in cubic 
feet per minute from an initial absolute pressure P a to a final 
pressure P 2 and deliver it at that pressure into the receiver, is 
the sum of the horse-power required in each of the two cylinders. 
In Article 60 it was shown that for a two-stage compressor the 
ratio of compression in each cylinder must be equal to the square 
root of the total ratio of compression, that is: 

-©' 

The horse-power required in each of the two cylinders is there- 
fore 

UlnVaPa r/P 2 \2 x ^T -i 
Horse-power = 88|000(fl _ 1) |_ \pj ~ 1 J 

And for the two cylinders the horse-power is just twice that 
amount. 

69. Theoretical horse-power — two-stage compression and 
delivery. 

144 n V a Pa r/Pi\^" ,1 
Horse -P° wer = 2 33,000 (n-l)LVpJ _1 J 

in which V a = volume of free air in cubic feet per minute, taken 
into the low-pressure cylinder (1). 
P a = initial absolute pressure in pounds per square inch 
in the low-pressure cylinder (1). 



56 COMPRESSED AIR 

P 2 = final absolute pressure in pounds per square inch 
in the high-pressure cylinder (2). 
n = exponent of adiabatic compression ( = 1.406). 
In the same manner we find for: 

70. Three-stage compression 

Horse - power==3 33,000(n-l)LlpJ - X J 



71. Four-stage compression 



n-l 



HorSe - pOWer = 4 33 ; 000(n-l)L(pJ - X J 

The theoretical mean gage pressure in pounds per square inch 
is for : 

72. Two -stage compression 

73. Three-stage compression 

Columns 7, 10, and 13 of Table V give the theoretical horse- 
power required at sea level to compress adiabatically and deliver 
1 cu. ft. of free air per minute by two-, three-, and four-stage 
compression. 

FINAL VOLUMES AND TEMPERATURES OF AIR IN STAGE 
COMPRESSION 

73A. Two-stage Compression. — On its passage from the 
low-pressure cylinder via the intercooler to the high-pressure 
cylinder, the air is cooled under constant pressure to initial 
temperature. On entering the high-pressure cylinder its volume 
Vi will therefore be equal to a volume, the intake-air V a would 
occupy had it been compressed isothermally in the low-pressure 
cylinder. According to Boyle's law this volume is 

V l = V a ^ (1) 



TWO-STAGE AND MULTI-STAGE COMPRESSION 57 

In the high-pressure cylinder volume V\ is compressed adia- 
batically to a volume V 2 and to an absolute pressure Pi. 

Therefore fj-© 1 

Introducing value of Vi from (1) and value 
Pi = VPaP2 from (3), Art. 60, 

n + l 

we get F 2 =F (J-J 2n (2) 

The absolute temperature of the discharge air will be the 
same as temperature Ti of the air when leaving the low-pressure 
cylinder, the ratio of compression being the same in both cylinders. 

According to (11), Art. 41 



Introducing Pi = VPaP-z 



we get T 2 =T a (^j ^ (3) 

By similar deductions we obtain analogous values for three- 
and four-stage compression as indicated in Table VIII. 

74. Modified Power Values for Practical Problems. — In the 
preceding theoretical formulas no allowance has been made 
for clearance, the heating of the in-take air and the friction of 
the compressor. As previously stated, the first two items are 
negligible as far as they affect power consumption. For fric- 
tion an additional allowance of from 7 to 15 per cent, of the 
theoretical horse-power is usually made in practical compres- 
sor calculations. 

75. Advantages of Multi-stage Compression. — The principal 
advantage of compound or multi-stage compression over single- 
stage compression lies in the saving of energy by reducing the 
heat of compression as pointed out above. Other important 
advantages due to compounding may be summed up as 
follows : 

a. Reduced Strain on Machine. — This will appear from the 
following illustration: 

Consider two compressors, compressing air to 120 lb. gage, 
one compressor having a single air cylinder of the usual pattern, 



58 COMPRESSED AIR 

the other having compound cylinders. With a piston of 100 
sq. in. in area, the maximum resistance which the single-stage 
compressor must overcome, would be 12,000 lb. 

Let us now consider a two-stage compressor in which the area 
of the low-pressure cylinder piston is again 100 sq. in. and that 
of the high-pressure cylinder one-third, or 33 1/3 sq. in. In 
the low-pressure cylinder the air is compressed to about 30 lb. 
Since this pressure of 30 lb. acts on the back of the piston in the 
high-pressure cylinder, it assists the machine, and the net re- 
sistance of forcing the air from the larger into the smaller cylinder 
is equal to the difference in the areas of the two pistons (which is 
66 2/3 sq. in.) multiplied by 30 lb. This equals 2000 lb. 

In the smaller or high-pressure cylinder the maximum re- 
sistance to overcome is 100X33 1/3 = 3333 lb., and the sum 
of the two resistances at the time of greatest effort in the two- 
stage compressor is 5333 lb. as compared with 12,000 lb. in the 
single-stage compressor, representing a reduction in strains of 
more than one-half. 

b. Improved Steam Economy. — The more equable distribution 
of the load throughout the stroke greatly reduces the danger of 
centering. This permits an earlier cut-off in the steam cylinder, 
resulting in a greater steam expansion. With properly designed 
inter-coolers the piston speed can be increased without danger 
of overheating the cylinders. Increased piston speed is in itself 
a factor in steam economy, since it reduces leakage and con- 
densation in the steam end of the compressor. 

c. Increased Safety and Ease of Lubrication. — When high 
final temperatures prevail, part of the lubricating oil vaporizes, 
and the wear on piston and cylinder becomes rapid. Under 
exceptional circumstances the combination of air and oil vapor 
and other combustibles may reach the proportions of an explo- 
sive mixture and, if the compression temperature reaches its 
ignition point, an explosion may result. Such accidents are, 
however, very rare even in single-stage work; in multi-stage 
compression, with proper inter-cooling and proper attention they 
are practically impossible. 

If the work of compression has been divided equally between 
the cylinders by a correct proportioning of their diameters, 
and if the inter-coolers are properly designed, the final tem- 
perature in each cylinder will be the same, and it will be much 
lower than if compression was completed in one cylinder. To 
illustrate: 



TWO-STAGE AND MULTI-STAGE COMPRESSION 59 

In compressing air at atmospheric temperature of 60° Fahr. 
to 100 lb. pressure in a two-stage compressor, the air is com- 
pressed from atmospheric pressure to 26 1/2 lb. in the in-take 
or low-pressure cylinder, and is delivered to the inter-cooler at 
this pressure and at 240° Fahr. If all the heat of compression is 
taken out by the inter-cooler, it is admitted to the high-pressure 
cylinder at atmospheric temperature and is then compressed 
from 26 1/2 lb. to 100 lb. and delivered to the receiver at a tem- 
perature of 240° Fahr. (Radiation and cooling by water-jack- 
ets not considered.) 

In a single-stage compressor the. air is compressed from 
atmospheric pressure to 100 lb. in one cylinder and reaches the 
receiver at a temperature of 482° Fahr. 

d. Greater Effective Capacity in Free Air. — Clearance loss in 
an air compressor is principally a loss in capacity, and affects 
only the in-take cylinder; it increases with the terminal pressure 
in this cylinder. Since in compound compression the terminal 
pressure in the low-pressure cylinder is much lower than in the 
single-stage machine, the air confined in the clearance spaces, 
when expanded down to atmospheric pressure, occupies com- 
paratively little space. Consequently the in-flow of air through 
the suction or inlet valves begins at an earlier point in the stroke 
than it would in the single-stage compressor, which results in a 
greater volumetric efficiency of the compound compressor. 
(See discussion of indicator cards in Chapter VIII.) 

e. Dryer Air. — The air delivered by a compound compressor 
is dryer than that furnished by a single cylinder. Under con- 
stant pressure, the power of air to hold vapor decreases with its 
temperature, and during its passage through the inter-cooler 
much of the original moisture in the air is precipitated. Conse- 
quently less trouble is experienced from condensation in the 
discharge pipe, and the danger of freezing up the exhaust ports 
of machines using compressed air is greatly reduced. 

76. When to use Two- and Multi-stage Compression. — 
Below and up to 60 or 70 lb. terminal pressure, the adiabetic 
loss is comparatively trival, and within this limit and at low 
altitudes, single-stage compressors are commonly employed. 
Between 60 and 100 lb., the amount of fuel is usually the deter- 
mining factor, though high altitude may also enter into the ques- 
tion. Above 100 lb. both safety and economy speak for two- 
stage and above 500 lb., for multi-stage compressors. 



CHAPTER VII 
EFFECT OF ALTITUDE ON AIR COMPRESSION 

77. Volumetric Efficiency. — The volumetric efficiency of a com- 
pressor, expressed in terms of free air, is the same at all altitudes 
because the piston displacement in a cylinder of a given size is 
the same. But the volumetric efficiency, expressed in terms of 
compressed air, decreases as the altitude increases. 

Since the density and hence the atmospheric pressure de- 
creases with the altitude, a compressor located at an altitude 
above sea level takes in at each revolution a smaller weight of 
air at a lower pressure than at sea level, and the early part of each 
stroke is occupied in compressing the air from this lower pressure 
up to the sea level pressure. In other words, the free air taken 
into a cylinder per stroke being less dense at an altitude (due to 
lower initial atmospheric pressure) it will be compressed into a 
smaller space for a given terminal pressure. 

Example. — Five-hundred cubic feet of air at atmospheric pressure 
at sea level (14.7 lb.), compressed isothermally to 80 lb. gage, occupies 
a volume of 

500X 80TK7 = 77 - 6 CU - ft 

From Table VI the atmospheric pressure at an altitude of 10,000 ft. 
is 10.07 lb. and 500 cu. ft. of air, compressed isothermally to 80 lb. gage 
at that altitude would occupy a volume of 

500X 80Tfo7= 55 - 9cU - ft - 

That is, the volumetric efficiency in terms of compressed air of a com- 
pressor performing the above work at an altitude of 10,000 ft. is only 
72 per cent, of what it would be at sea level. 

In order, therefore, that an air compressor at an altitude may deliver 
a volume of compressed air per stroke equal to that which it would 
deliver at sea level, the in- take cylinder of the altitude compressor must 
be proportionally larger than that of a compressor at sea level. 

78. Multipliers for Altitude Computations. — Referring to the 
preceding example, multipliers may be computed for determin- 

60 



EFFECT OF ALTITUDE ON AIR COMPRESSION 61 

ing the volume of free air at various altitudes which, when com- 
pressed to various pressures, is equivalent in effect to a given 
volume of free air compressed to the same pressure at sea level. 

Let V = a certain number of cubic feet of atmospheric air to 
be compressed simultaneously at sea level and at an 
elevation above sea level, 
P a = absolute pressure of atmospheric air in lbs. per square 

inch at sea level (14.75 lb.), 
Pi = absolute pressure of atmospheric air in lbs. per square 
inch at the given elevation, 
p = gage pressure to which air is being compressed, 

then the volume V\ which the air occupies after being compressed 
to p pounds gage at sea level: 

Pa 



Vl = V 



(V+Pa) 



And the volume V 2 which the air occupies after being compressed 
to p pounds gage at the elevation: 

In order that V 2 may be equal to V\ it must be multiplied by 
a multiplier "M " which we find as follows: 

MV 2 = Vi 

Substituting values 

P + Pl P + P a 

Whence ^=^7 E xS 

Pl(p + P a ) 

Example. — What is the multiplier for a volume of air at 5000 ft. 
elevation and for a pressure of 80 lb. gage. (See Table VI.) 

P«(p+Pi) _ U/75 (80+12.20) 
Pi(p+P-j 12.20(80+14.75) 

If for instance we wish to know the volume of free air which after 
being compressed to 80 lb. gage at an altitude of 5000 ft., has the same 
effect as, say 100 cu. ft. of air compressed to 80 lb. gage at sea level, we 
find it by multiplying 100 by 1.178. 

Thus, 100X1.178 = 117.8 cu. ft. 



62 COMPRESSED AIR 

79. Power Required for Altitude Compressors. — To compress 
a given volume of free air taken in by a compressor of given size 
to a given terminal pressure takes less power at an altitude than 
at sea level. The air being lighter and less dense, its volume at 
the desired terminal pressure will be smaller, that is, the final 
pressure is reached at a later point in the stroke. Hence the mean 
pressure is less and so is the total power required to compress the 
quantity of air taken into the cylinder. 

But, in order to produce at an altitude a quantity of com- 
pressed air which is equivalent in effect to air at sea level, more 
power is required, because the reduction in power referred to 
above is not proportional to the increase in volume necessary to 
equal sea-level performance. 

Example. — Using formula, Article 68, we find that to compress by 
two-stage compression 100 cu. ft. of free air per minute at sea-level 
pressure (14.7 lb.) to 100 lb. gage and deliver it into the receiver re- 
quires 15.80 h.p. At an altitude of 10,000 ft., where the atmospheric 
pressure is 10.07 lb., it would require only 12.50 h.p. 

But from Table VI, a quantity of air which at an elevation of 10,000 
ft. is the equivalent of 100 cu. ft. of free air at sea level would occupy 
a volume of 140.4 cu. ft. To compress this quantity to 100 lb. gage and 
deliver it into the receiver would require: 

140 4 

^p 12.50 = 17.55 h.p. 

This shows that in this case 1.75 additional horse-power are required 
at 10,000 ft. elevation to produce the same effect as at sea level. 

80. Stage Compression at High Altitudes. — From what has 
been said of the effect of altitude on air compression, it becomes 
evident that stage compression at altitudes results in even larger 
percentage of saving of power than is possible at sea level. 

Referring to Table V, it requires 0.182 h.p. at sea level to com- 
press in one stage 1 cu. ft. of free air per minute to 100 lb. gage 
and deliver it into the receiver. Two-stage compression would 
consume only 0.158 h.p. which means a saving of 0.024 h.p. or of 
13 per cent, in favor of two-stage compression. 

At 9000 ft. above sea level the equivalent of 1 cu. ft. of air 
at sea level is 1.356 cu. ft. and the atmospheric pressure is 10.46 
lb. (from Table VI). Horse-power required to compress 1.356 
cu. ft. of free air per minute to 100 lb. gage at 9000 ft. elevation 
and deliver it into the receiver: 



EFFECT OF ALTITUDE ON AIR COMPRESSION 63 

For single-stage compression, 0.21 h.p. (from Article 47) 
For two-stage compression, 0.17 h.p. (from Article 68) 

which means a saving of 0.04 h.p. or of 19 per cent, in favor of 
two-stage compression at an altitude of 9000 ft. 

81. It has been pointed out heretofore that the volumetric 
efficiency of a compressor is higher in two-stage than in single- 
stage compression, owing to the smaller volume which the ex- 
panded clearance air occupies. This volume being a function 
of the ratio of compression, it follows that at high altitudes, 
stage compression can be profitably used for lower terminal pres- 
sures than is customary at sea level. 

To illustrate: The ration of compression at sea level in com- 
pressing to 90 lb. gage is 

90+14 ^-7 12 
14.7 ~ 7 ' lZ 

The same ratio would obtain at an elevation of 10,000 ft. in 
compressing to 61.63 lb. gage; for 

61.63 + 10.07 



10.07 



= 7.12, 



which means that, if it pays to use two-stage compression at sea 
level in order to reduce clearance losses when compressing to 90 
lb. gage, it would pay to do so at 10,000 ft. elevation, when com- 
pressing to 62 lb. gage. 

The theoretical power required to compress a certain quantity 
of air at an altitude above sea level can be deduced from the 
formulas for the mean gage pressure and for the horse-power 
given under Adiabatic Compression (Articles 46, 47 and 68 to 
72) by substituting for Pi or P a , respectively, the atmospheric 
pressure at the given altitude. The latter may be found from 
Table VI or calculated from formula (2), Article 4. 

Manufacturers usually build special compressors for high alti- 
tudes which are designed to meet the demands made on a plant, 
located at considerable elevation above sea level. 



CHAPTER VIII 
THE COMPRESSED AIR INDICATOR CARD 

82. Inasmuch as the work performed in the air cylinder of a 
compressor depends on so many variable and interdependent 
conditions, it can only be studied successfully from an indicator 
card, or still better from a number of indicator cards taken from 
the air cylinders of a compressor when in actual service. 

It is assumed that the reader is familiar with the methods of 
taking an indicator card and of calculating from it the mean 
pressure, the horse-power, and the volumetric efficiency. There 
are a number of excellent books available which discuss this 
subject in detail, to which the reader is referred. 

Besides the facts regarding power consumption, indicator dia- 
grams also convey information regarding the working of valves, 
the volume of air taken in and compressed, the effect of clearance, 
the efficiency of the cooling devices, and the correct or incorrect 
proportioning of the air cylinders. 

Unfortunately, indicator cards do not register temperatures 
and thus offer no means for determining directly the useful 
capacity of the compressor, expressed in number of pounds of 
free air at outside temperature compressed and delivered per 
unit of time. The latter is the only correct estimate of compressor 
capacity for the reason that before the air is used in the air engine, 
it has assumed outside temperature and any increase in volume, 
due to heat which the air may have received before or during 
compression, is only temporary and is subsequently lost for 
useful purposes. 

Therfore an indicator card which shows high volumetric effi- 
ciency is in itself no proof of the ultimate merits of a compressor 
as far as capacity is concerned. 

In Article 53 it was shown that inlet valves, which prevent 
ready admission of air, reduce the volumetric efficiency. This 
is shown on the air card by the suction line falling considerably 
below the atmospheric line. On the other hand, an air card 
taken from a compressor with leaky inlet valves may show a 

64 



THE COMPRESSED AIR INDICATOR CARD 65 

large volumetric efficiency due to the fact that some of the 
clearance air escapes through them into the atmosphere and the 
expansion line CG (Fig. 8) falls sooner, thus increasing the dis- 
tance RG without, however, increasing the useful quantity of air 
compressed. 

In the same manner will leaky discharge valves, leaky pistons 
and inter-coolers show an apparent increase in volumetric effi- 
ciency while the actual quantity of air delivered is diminished. 

Air cards, showing practically isothermal compression lines, 
are frequently the result of a leaky piston and not of superior 
workmanship in the construction of the compressor. A leaky 
piston will reduce the compression line as fully or more effectually 
than any cooling of the air can do, so that anyone not familiar 
with the tricks of an air card may easily be misled in his judgment 
of the merits of a machine from the indicator card alone. 

Evidence of a leaky piston is usually given by a card showing 
the admission line above the atmospheric line during the entire 
stroke. 

From what has been said, it is evident that great caution must 
be exercised in interpreting an air card. To do this correctly, it 
is necessary to know what positive information an air card will 
give and to bear in mind that it does not tell the whole story. 

In the following articles a few air cards and their interpretation 
are given with the object of assisting the student of this subject 
in reading and interpreting similar cards. 

83. Air Card of a Single-stage Compressor. — Fig. 12 is the 
facsimile of an indicator card taken from the air cylinder of a 
single-stage compressor. On this card the actual compression 
curve AC lies between the adiabatic curve AB and the isothermal 
curve AD. The gage pressure of the air in pounds per square 
inch at any point M of the stroke is measured by the line MN. 
The card shows the usual performance of a compressor of this 
type. When the piston has reached point C the air has reached 
receiver pressure (61 lb. gage on the card illustrated). 

Owing to the weight of the discharge valves and the tension of 
the springs, the pressure in the cylinder usually rises a few pounds 
above the receiver pressure before the valves open, as shown at 
E. From this point to the end of the stroke the pressure drops 
to the receiver pressure. The wavy shape of the delivery line is 
mainly due to the fluttering of the discharge valves. 

At the end of the forward stroke at F the piston comes to a 

5 



66 



COMPRESSED AIR 



standstill. The discharge valves close and as soon as the piston 
commences the return stroke, the compressed air that was left 
in the clearance space begins to expand until it reaches atmos- 
pheric pressure at G. At this moment the inlet valves should 
open, but they are usually held for a moment against their seats 
by the tension of the springs. A partial vacuum is thus created 
behind the receding piston, causing the expansion line FG to 
drop below the atmospheric line as shown at 0, whence it returns 
to the atmospheric line as soon as the valves open. 




-PI8T0N DISPLACEMENT 

Fig. 12. 



Free air is now admitted and if the inlet area is not restricted, 
the admission line will closely follow the atmospheric line from 
G to A. A considerable drop below the atmospheric line indi- 
cates that air is not admitted as freely as should be. This may 
happen when the slowing down of the piston at the end of the 
stroke permits the springs to close the inlet valves before the 
piston has completed its stroke. This reduces the volumetric 
efficiency of the compressor to the volume GR, because on the 
next forward stroke the piston must travel a distance A R before 
the atmospheric line is reached and before actual compression 
begins. 

The line HG measures the extra volume taken up by the clear- 
ance air after expansion. It represents a loss which can be 
minimized by reducing the clearance space but cannot be avoided 
altogether. Theoretically, the loss is one of capacity only and 
not of power; for, although this air required work in compressing 



THE COMPRESSED AIR INDICATOR CARD 67 

it to receiver pressure, in expanding it helps to compress the air 
on the other side of the piston. (See Article 52.) 

84. Air Card of a Two-stage Compressor. — Fig. 13 shows the 
combined cards taken from the crank-end of a two-stage com- 
pressor. 

Low-pressure air cylinder 32 1/2X48 in. 

High-pressure air cylinder 20 1/4X48 in. 

Piston speed 480 ft. per minute. 

Piston displacement per stroke 22. 13 cu. ft. 

Pressure of inlet air 14 . 00 lb. absolute. 

Discharge pressure 78 . 00 lb. gage. 

Volumetric efficiency (from card) 95 per cent. 

Actual free air (from card) 2519 cu. ft. per minute. 

Air horse-power (from card) 416. 

The theoretical horse-power required for single-stage com- 
pression of the same quantity of air is 384, showing an excess of 
power consumed over a single-stage compression, amounting 
to 8.5 per cent. 

This card, which is one of many that may be taken from other- 
wise well-built two-stage compressors, shows that in actual prac- 
tice two-stage compression does not always result in a saving of 
power as would appear from theoretical calculations. 

Whenever there is an overlap of the indicator cards taken 
from the low- and high-pressure cylinders of an air compressor, 
or when they run above the discharge pressure or materially 
below the in- take (atmospheric) pressure, there is power used in 
excess of the saving due to inter-cooling. Two-stage compressors 
giving cards such as shown in Fig. 13 fail to realize a saving of 
power over single-stage compressors usually through one or the 
other of the following defects. 

o. Cylinders not properly proportioned for the prevailing com- 
pression ratio. In the case illustrated, the high-pressure cylinder 
seems to be too small and the low-pressure cylinder has to per- 
form too much of the compression work. 

6. Inter-cooler too small or inefficient. The theoretical sav- 
ing of power is based on perfect cooling of the air to initial tem- 
perature after leaving the low-pressure cylinder. Failure on the 
part of the inter-cooler to do this will increase the work in the 
high-pressure cylinder. 

c. Valve areas too small and air passages restricted. Re- 



68 



COMPRESSED AIR 



stricted inlet valve area in low-pressure cylinder not only in- 
creases the work to be done but also reduces the compressor 
efficiency. Restrictions in the high-pressure inlet, and low- 
pressure discharge valve areas, and in the inter-cooler and its 
piping, produce an excess in the discharge pressure from low- 
pressure cylinder to inter-cooler and a depression in the suction 
line of high-pressure indicator cards. The result of this is a 



100 LBS. 



.RECEIVER PRESSURE 




CRANK END 

Fig. 13. — Combined Air Cards of a Two-stage Compressor. 



great overlap in the developed diagrams where the high- and low- 
pressure cards come together. These pressure losses also pro- 
duce an unequal distribution of the work in the two cylinders. 

From Article 60 the terminal pressure in the low-pressure 
cylinder should have been: 



Pi = VPoP2 = V14.0(78 + 14) = 36 lb. absolute. 

A glance at the diagram shows that the discharge valves of 
the low-pressure cylinder did not open until the pressure has 
reached nearly 50 lb. absolute, indicating a large waste of energy. 

85. Fig. 14 shows the combined air cards, taken from both 
the head-end and crank-end of a two-stage Nordberg com- 
pressor. A comparison of these cards with the one shown in Fig. 13 



THE COMPRESSED AIR INDICATOR CARD 



69 




I 1 S 1 S> gl S 1 S 1 S 1 8 1 8 1 



70 COMPRESSED AIR 

reveals far more perfect conditions. The in-take line of the low- 
pressure cylinder closely follows the atmospheric line, showing 
unrestricted in-take areas. The compression line of the high- 
pressure cylinder begins at the intersection of the isothermal 
compression line with the delivery line of the low-pressure cylin- 
der, showing perfect inter-cooling; and the fact that the dis- 
charge line of the low-pressure cylinder is practically identical 
with the in-take line of the high-pressure cylinder and is nearly 
a straight line, shows satisfactory condition of valves and proper 
proportioning of the cylinders for the prevailing ratio of com- 
pression. 

Low-pressure air cylinder 29X42 in. 

High-pressure air cylinder 19X42 in. 

Piston speed. . . 364 ft. per minute. 

Piston displacement per stroke 15.84 cu. it. 

Pressure of inlet air • 14 . 7 lb. absolute. 

Discharge pressure 80 . gage. 

Volumetric efficiency (from card) 98 . 7 per cent. 

Actual free air per minute (from card) . . . 1611 cu. ft. 

Air horse-power (from card) 237 

The theoretical horse-power required for single-stage com- 
pression of the same quantity of air is 256, showing a saving of 
power over single-stage compression amounting to 8 per cent. 



CHAPTER IX 

COOLING WATER REQUIRED IN COMPRESSION; EFFICIENCY 

OF COMPRESSOR PLANT; AIR-COMPRESSOR 

EXPLOSIONS 

86. Amount of Cooling Water Required in Air Compressors. 

Let W = weight of required water in pounds per unit of time. 
w = weight of air in pounds to be cooled per unit of time. 
t = initial temperature of free air in degrees Fahr. 

= initial temperature of cooling water in degrees Fahr. 
h = final temperature of compressed air in degrees Fahr. 
s = specific heat of air. 

We have seen that the amount of heat required to raise the 
temperature of,l lb. of water 1° Fahr. is 1 B.T.U. Accordingly, 
the number of pounds of water required to abstract a quantity 
of heat from any substance without raising the temperature of 
the water more than 1° Fahr. is equal to the number of B.T.U.'s 
to be abstracted. 

Now, if "w" pounds of air have been heated during compres- 
sion from an initial temperature t° to a final temperature ti° 
Fahr., the rise in temperature is (h — t)° Fahr. 

In order to cool this quantity of air to initial temperature, 
we must abstract from it an amount of heat, which, expressed 
in B.T.U.'s, is 

B.T.U.'s = ti;(«i-Os (1) 

This also represents the number of pounds of cooling water 
required, having the same initial temperature as the in-take air. 
Therefore 

W = w(h-t)8 (2) 

Since in compressor practice the air is cooled under constant 
pressure, the specific heat is from Article 8. 

s = 0.2375 

Example. — How many gallons of water per minute are required to 
cool to initial temperature 800 cu. ft. of free air per minute, compressed 

71 



72 COMPRESSED AIR 

to 80 lb. gage? Initial temperature of water and free air to be 60° 
Fahr.; temperature of water when leaving cooling devices to be not 
more than 61° Fahr. 
One pound of water = 0.12 gal. 

From column 9, Table V, we find the final temperature of air, com- 
pressed adiabatically in two stages to 80 lb. gage = 224° Fahr., which 
is an increase of (224-60) = 164°. 

From Table I, 800 cu. ft. of free air at 60° Fahr. weigh 800X0.0764 = 
61.121b. 

Therefore B.T.U.'s to be abstracted from air = 61.12X164X0.2375 = 
2380 and water required per minute = 2380X0.12 = 290 gal. 

In practice it is usually deemed satisfactory to allow an increase of 
temperature in the water, amounting to from 10 to 25 degrees, thereby 
reducing the quantity of cooling water required. If the initial tempera- 
ture of the water is 60° Fahr. when entering and 70° Fahr. when leaving 
the cooling devices, then every pound of water has absorbed 10 B.T.U.'s 
from the heated air and the number of pounds of water required in this 

290 
case will be only one-tenth of the quantity stated above, that is -j^r = 30 

gal. per minute (nearly). 

In actual compression, considerable radiation is going on and the 
final temperature of the compressed air is less than the theoretical tem- 
perature taken from the table. It is therefore safe to divide the theo- 
retical quantity of water as found from equation (2) by two or even 
three. 

For the case assumed, the minimum quantity of cooling water re- 
quired would therefore be: 

30 

-^-=10 gal. per minute. 

When water is scarce and has to be used over and over again, it be- 
comes necessary to cool it by artificial means to initial temperature 
before returning it to the cooling devices of the compressor. The 
greater its temperature when leaving the compressor, the slower and the 
more expensive will be the artificial cooling which is usually accomplished 
in so-called cooling-towers. Hence the practical limit of permissible 
increase in temperature, which is, as stated above, from 10 to 15 degrees 
above initial temperature. 

EFFICIENCY OF A PLANT FOR THE PRODUCTION OF 
COMPRESSED AIR 

87. Compressor efficiency is a term which is used rather 
loosely. Usually it is meant to designate the ratio between 
the theoretical power required to compress and deliver a certain 



EFFICIENCY OF A COMPRESSOR PLANT 73 

quantity of free air and the actual power expended. This is the 
mechanical efficiency of a compressor, strictly speaking. Volu- 
metric efficiency is explained under Article 53. 

What is important to know in the end is the efficiency of the 
complete plant for the production of compressed air, including 
the compressor itself with all its accessories such as air in-takes, 
inter-coolers, after- coolers, receivers, and so forth. 

We wish to know the power value of a certain quantity of 
compressed air after it has left the compressor and has cooled 
down to initial temperature. All energy expended beyond that 
value is lost for useful purposes. This loss is chargeable to the 
installation for the production of compressed air and its total 
amount measures the lack of efficiency of the installation. 

To compute the efficiency, we must take into account all 
losses that occur from the moment the air is taken into the 
cylinder of the compressor until it is delivered into the pipe line at 
practically initial temperature. 

These losses have been frequently alluded to in previous 
articles. They are as follows : 

1. Losses are due to initial temperature of the in-take air. 
It has been pointed out that under ordinary circumstances air 
will, after compression and before use, assume the temperature 
of natural objects. For compressor computations this is usually 
taken as 60° Fahr. 

We will assume that we wish to produce a volume of air com- 
pressed to 70 lb. gage which, after having cooled down to 60° 
Fahr., is the equivalent of 500 cu. ft. of free air per minute. If the 
in-take air has a temperature of 60° Fahr., the amount of air to be 
compressed is, of course, 500 cu. ft. per minute. To compress 
adiabatically in one stage 500 cu. ft. of free air per minute to 70 
lb. gage, and deliver it into the receiver, requires (from column 4, 
Table V) theoretically 74.00 h.p. 

If the temperature of the in-take air had been 100° Fahr. and 
500 cu. ft. of it were cooled down under constant pressure to 60 
degrees, they would occupy a volume of: 

T _ 500X (60+461) 
Fl ° (100+461) ° 464 cu - ft -> 
which is less than the required volume. 



74 COMPRESSED AIR 

Therefore, in order to have in the end a volume of compressed 
air which when cooled to 60° Fahr. is the equivalent of 500 cu. ft. 
of free air, we should have compressed more than 500 cu. ft. of 
the 100 degree air. The volume to be compressed in this case 
is: 

_ 500X (100+4 61) 

y= (60+461)~ = 538cU ' ft - 

To compress adiabatically in one stage 538 cu. ft. of free air per 
minute to 70 lb. gage, and deliver it into the receiver, requires 
(from column 4, Table V) theoretically 79.62 h.p. This is an 
increase of 7 per cent, in the required power due to an increase 
of 40 degrees in the temperature of the in-take air, or 1 per cent, for 
every 6 degrees. 

This points to the advantage of bringing cool air to the 
machine. Neglect to do so will result in power loss as pointed 
out, which must be charged to the compressor plant as a whole. 

2. Losses are due to the in-take air being heated as it passes 
in very thin streams over the valve surfaces which have been 
heated by the air under compression. These losses are difficult 
to ascertain, since an indicator card gives no hint whatever of 
their occurrence. Indicators record pressure only, not tempera- 
tures. These losses add to those stated under (1), and may be 
considerable. 

3. Losses are due to imperfect valves. Poppet valves being 
operated by strong springs are liable to throttle the inlet air, 
the effect of which is scarcely noted on ordinary indicator 
cards. Nevertheless, such throttling results in the creation of a 
partial vacuum which cuts down the capacity as pointed out 
under Article 53 and being a drag on the machine consumes more 
power in addition to power required for the extra number of 
revolutions needed to make up for capacity loss. 

4. Losses are due to clearance. They have been discussed in 
Article 52. The ultimate effect of clearance is the delivery, into 
the receiver, of a volume of air smaller than that which has 
actually been compressed at each stroke of the piston. 

5. Losses are due to the generation of heat during compression 
which is afterward dissipated and completely lost for useful 
work. These are by far the most serious losses incident to air 
compression, and have therefore received close attention by 
designers and builders of air compressors. All attempts have 



EFFICIENCY OF A COMPRESSOR PLANT 75 

been directed toward the accomplishment of isothermal com- 
pression by the introduction of water-jackets and of inter-coolers 
in stage compressors. At the present state of the art, these 
losses are unavoidable. But by judicious selection of com- 
pressors provided with adequate cooling devices they can be 
reduced to a minimum. 

6. Losses are due to imperfect design, carelessness in handling, 
neglect in properly lubricating, stopping leaks, and removing 
worn-out parts of the compressor. 

Example. — Let the piston displacement of the air cylinders of a single- 
stage compressor be 10 cu. ft. and the temperature of the free air taken 
into this cylinder be 60° Fahr. In passing over the heated inlet valves 
and coming in contact with the heated cylinder walls, its temperature 
will rise, let us say, to 70° Fahr. We have no means at present to 
measure this accurately. The theoretical power required to compress 
in one stage adiabatically 10 cu. ft. of free air to 70 lb. gage and deliver 
it into the receiver is: 



W n = 1U £ P : > I ( ",, ) -i| ft.-lb 



To this we will add 15 per cent, for friction etc., which gives 

W n = 55,600 ft.-lb. (1) 

Neglecting jacket cooling and radiation, the temperature of the com- 
pressed air will be: 

n-l 

T 1 = t(^) " = (70+461) x(^y) =882 degrees absolute. 
The volume F 2 into which the air has been compressed will be : 



i 

0.71 



If the clearance of the compressor is 2 per cent., the actual volume of 
compressed air delivered into the receiver is not V 2 but: 

F 3 = 2.88-^ X2 = 2.68 cu. ft. 

It is true that the expanding clearance air helps to compress air on the 
return stroke of the piston, that is, the value of Wn as stated in equa- 



70 



t n\U , MR 



tion (1) will be sou. arance air 

|roef absolute, in mingling with U 
romii.j 

we have allowed for heating durum 
valves, BO. Wt .-hall neg'.- 

required p 

I 

grees absolut 

• ase to a pressure /', which we deduce 

. 



/' I'. 






/>,-(70+U lute. 

at an absolute 

initial pw ui 
cally I :' perform work, which • 

formal 110. 



IT 1U ' } '> V > 1 i 1 ' \ 

-'"■"; ']- Wf ,,, 

r value of the compressed air which w 

out to determine. 

Installation for I - is in 1 1 

und< ■ 



20,000 
56.000 






Und. r ' 

permlun omprew 

will t>e leas than 882 degrees absolute because of jack* 

and i n> plants the affl y leaa. 

than 
stage compressors, bco. iiprcaakxi 

is |. vs. Hot a stage compressor is a mor 
tnted when 



Ml:-< OMPRl 
Dg costs tatei fur invest- 

omprei atly sho 

r than a - -age 

pter \'I l <.) 

AIR-COMPRESSOR EXPLOSIONS 

88. In gi neral, an explosion is due to quid 
lowed I • olume of gas, which, if 

fined, niddenly i r i « i re against th< 

■ 
I in in an air compress) 

air cylinder i 
i. \ combustible substance in ■ finely divid 
permit | ly instantaneous ignition of the 

■ ration ol a large vo iraa. 

_' Of air or oxygen in the proper proportion to completely 
oxidise the combustible, form an explosive naixl . 

\ temperature high enough to ignite the mixture, 
any one of the above three oondif 
mal plosion impossible. This point 

i. < Combustibles: The only combustible substance purp 
introduced into the air cylinder i ^pressor ia the lul>r: 

ing oil. Incidentally, what. mbustible substai 

• mi.. 1 in the atmosphere will be drawn into the cyiinder 
during the suction itroki , 

!i . q>losion will dally increased. 

the ingn iting oil 

will oil under the influence of In 

leh 
i ai to make an explo I • ire with tin- air. 

mbustible n 
(■satisfied I 

• 

• m th« 

^4 use of lubi 
•Ice of the i 
with the aii improbal 

tie ever eauses an explosion It 



78 COMPRESSED AIR 

is nevertheless possible that in an air cylinder with leaky valves 
and piston, enough of these vapors may eventually accumulate 
to at least assist in an explosion. 

It is more probable that carbonaceous matter in a finely divided 
or porous state is the chief cause of an explosion, when present 
in the proper proportion and exposed to abnormal temperatures. 

2. The proportion of combustible matter and air or oxygen, 
required to form an explosive mixture, is dependent on the nature 
of the combustible. We are fairly well acquainted with these 
proportions when the mixture takes place under atmospheric 
pressure. What they are under the high pressures prevailing 
in the cylinder of an air compressor is a question which can only 
be answered when more reliable data become available. 

3. The temperature required to ignite an explosive mixture 
under atmospheric pressure we also know fairly well. Finely 
divided carbon, for instance, ignites at a temperature of 600° 
Fahr. Under high pressure, it is quite possible that ignition 
takes place at a temperature considerably below that. 

However conducive oil may be to an explosion, its use as a 
lubricant, and therefore the accumulation of carbonaceous matter . 
and the formation of vapors, cannot be avoided altogether. 
But by proper care and perfect cooling devices, the temperature 
can be kept within safe limits. To do this, we must know the 
conditions which cause abnormal temperatures. Chief among 
them are the following: 

a. When air is taken into the cylinder from a hot engine room 
or from the neighborhood of a boiler room. Other evil effects 
of such conditions have already been pointed out under Article 87. 

Air at a temperature of 150° Fahr. and compressed in one stage 
to, say, 75 lb. gage, would have a final temperature of 

T,= r(^)~"~ = (150+461) ( ^y 47 ) =1030° absolute 

= 569° Fahr. 

which even if reduced somewhat by water-cooling would come 
dangerously close to or exceed the ignition point of any explosive 
substance. 

b. When the maximum pressure for which the compressor is 
built is willfully or accidentally exceeded. The final temperature 
is thus raised to a point beyond the efficiency of the cooling ap- 



AIR-COMPRESSOR EXPLOSIONS 79 

pliances and will ultimately reach the ignition point of an ex- 
plosive mixture. 

c. When the pressure is exceeded by reason of a gradual ac- 
cumulation of carbonaceous matter of the oil in the discharge 
valves. This contracts the passage and requires higher pressure 
for the delivery of a certain amount of air in a given time, thus 
raising the temperature. 

d. When valves are not kept clean and pistons are permitted 
to wear loose, which causes leakage of compressed air into the 
in-take side of the cylinder. This is probably the most frequent 
source of excessive temperature. The leakage air expands to 
atmospheric pressure without doing work, hence loses none of 
its heat (see Article 118), and in mixing with the incoming free 
air it raises the temperature of the mixture which is to be com- 
pressed on the following stroke to a dangerous degree. 

The dangerous effect of leakage in the air cylinders of a com- 
pressor is shown in the following example : 

Example. — Let W = weight of a given quantity of atmospheric air, 
occupying a volume equal to the piston 
displacement. 
= unity (assumed) = 1 = TFi+l^. 
W\ = weight of atmospheric air which enters the 
cylinders at each stroke at an absolute tem- 
perature T\. 
= 1-T7 2 . 
W 2 = weight of leakage air, having an absolute tem- 
perature T 2 and which expands to atmospheric 
pressure upon entering the in-take side of the 
cylinder. 
Po = absolute pressure of atmospheric air in pounds 

per square inch. 
P 2 = absolute pressure of compressed air in pounds 
per square inch, 
c = specific heat of air. 
n = 1.406. 



It is evident that the total quantity of heat in the mixture W must 
be equal to the sum of the heat quantities contained respectively in 
W\ and in W 2 before mixing. If the absolute temperature of W has 
become T after the mixing of the leakage with the atmospheric air, 
then : 



SO COMPRESSED AIR 

Total heat in W = W T c 

Total heat in W x = WiT x c 

Total heat in W 2 = W 2 T 2 c 
and W T c = c(W 1 T 1 +W 2 T 2 ) 

Remembering that W = 1 and TTx = 1 — TT 2 
We find T = T 1 (1-W 2 ) + T 2 W 2 (1) 

If the temperature before compression is T , then the temperature T 2 
after compression to an absolute pressure P 2 according to equation (11), 
Article 41, is: 

Let the temperature of the in-take air be 60° Fahr. 
then T x = 60+461 = 521 degrees absolute. 

Let leakage air equal 15 per cent, of W 
W 1 

then W2 = To^ Xl5 = 100 X 15 = - 15 

Let the air be compressed to 85 lb. gage, 
then P 2 = 85+ 14.7 = 99.7 

If we assume the compressor to have made a number of strokes 
before leakage occurs, then] the temperature of the compressed air will 
be 447° Fahr. (Col. 8, Table III). If leakage now begins at a rate of 
15 per cent, we have T from equation (1) : 

T o = (60+461)(l-0.15)+0.15(447+461) =579 degrees absolute. 
If we compress this air to 85 lb. gage, its final temperature will be from 
equation (2): 

T 2 = 579 X6.782°' 29 = 1005 degrees absolute = 544° Fahr. 

Some of this compressed air leaks into the in-take side of the cylinder 
where we get an air mixture of the temperature: 

7\ > = (60+461)(l-0.15)+0.15(544+461) = 595 degrees absolute 
and this air compressed to 85 lb. gage will have a temperature 

T 2 = 595 X6.782 0>29 = 1037 degrees absolute = 576° Fahr., etc. 

This shows that the temperature in the cylinder is increasing with 
every stroke of the piston and in spite of the cooling devices will soon 
reach a point at which in the presence of combustible material and in- 
flammable vapors an explosion is likely to occur. 

The danger increases when the compressor is running at slow speed. 
Leakage is a constant quantity per unit of time. Hence in a slow-speed 
machine the percentage of leakage air per stroke will increase and that 
of the cool in-take air will decrease. As a consequence the tempera- 
ture of the mixture to be compressed on the next stroke will be propor- 
tionally higher, thereby increasing the danger of an explosion. 



AIR-COMPRESSOR EXPLOSIONS 81 

89. Compressors, using throttling devices for the regulation 
of intermittent demand, may under certain conditions develop 
dangerous temperatures. By throttling the inlet, the initial 
pressure is lowered, while the ratio of compression is increased. 
As a result, the final temperature will be considerably higher 
than under normal conditions, so high as to ignite any explosive 
substance that may be present in the cylinder. 

Example. — Let us assume that the output of a single-stage compressor, 
working against 60 lb. pressure is to be reduced by throttling to one- 
fourth of its full capacity. If atmospheric pressure is 14.7 lb. per square 
inch, the pressure of the in-take air will become: 

14-7 

—t—= 3.7 lb. per square inch, 



and the total ratio of compression: 

Pi 60+14.7 



= 20.2 



P 3.7 

If the initial temperature of the air is 70° Fahr., the final temperature, 
from equation (11), Article 41, will be: 



'Pi> 



0-29 



Tl==T (p) " =(70+461)20.2 "" =1270 degrees absolute, 809° Fahr. 

Although radiation and jacket-cooling will considerably reduce this 
temperature, the figures nevertheless indicate the danger connected 
with compression of rarefied air such as obtains in compressors regulat- 
ing the output by throttling the in-take. 

90. Prevention of Compressor Explosions. — Having pointed 
out the most likely causes of an explosion in a compressor, the 
means of prevention become self-evident. They consist first in 
guarding against accumulation of explosive substances in the 
air cylinder, and second in keeping down temperatures below 
the danger point. 

The first is accomplished by using a lubricant which does not 
precipitate its carbon contents at normal temperatures and by 
using it sparingly. Soapy water fed at intervals to the cylinder 
is good practice. Inspect the valves frequently and remove all 
accumulations of foreign substances. 

Abnormal temperatures are prevented by water-jacketing 
and inter-coolers, if they are of proper design and magnitude. 
Leaks in valves and piston, as pointed out, prevent the most 
perfect cooling devices from doing their duty. They should be 
stopped as soon as discovered. 



PART II 

THE TRANSMISSION OF COMPRESSED AIR 



CHAPTER X 
TRANSMISSION OF COMPRESSED AIR 

91. Compressed air, before being used in so-called air engines, 
has to be conveyed from the compressor room to the points of 
use in iron pipes of various dimensions. The question then arises : 
What should be these dimensions so as to satisfy the demand for 
compressed air at the discharge end of the pipe line? 

The solution of this problem requires, besides a knowledge of 
the behavior of compressed air flowing through a pipe line, a 
careful study of local conditions and a close comparison of first 
cost of installation with the ultimate operating expenses. 

92. The laws governing the flow of compressed air in iron 
pipes are far more elusive and complex than those for water, 
owing to the fact that compressed air is not a stable substance 
like water but changes its pressure, density, volume, velocity and 
friction at every point of the pipe line. 

Attempts to express these laws in simple formulas, which 
would hold good in all cases, seem therefore quite hopeless. 
The best that can be said of any of the formulas employed 
by engineers, is that the numerical results obtained from them 
will in most cases correspond only approximately with those 
obtained from actual practice. They must therefore be used 
with a great amount of caution. 

Before referring to these formulas, it is well to study the 
behavior of compressed air during its passage through a pipe line. 
We have seen that in order to cause air to flow from one point to 
another, there must be a difference of pressure in the air at those 
two points. That is, if we need air at a pressure of 80 lb. at a 
certain distance from the compressor, the pressure of the air as 
it leaves the compressor or receiver must be greater than 80 lb. 

This difference of pressure which is necessary to make the air 
flow, represents energy which does useful work, that is, it conveys 
the air from one place to another. It is therefore not a loss in 
the true meaning of the word. But air in its passage through pipes 
is subject to friction. To overcome this friction, energy in the 

85 



86 COMPRESSED AIR 

form of pressure is required, additional to that needed for keeping 
the air in motion. To produce this extra pressure in the air, 
power is consumed in the compressor which is an actual loss as 
there can be no useful return for it. 

Friction reduces the pressure of the air, and since the tempera- 
ture in the pipe can be assumed to be constant, this reduction of 
pressure increases the volume of the air. To force an increased 
volume of air through a pipe of the same diameter during the 
same time means increased velocity and this in its turn requires 
an additional power in the form of pressure. 

In general, the transmission of air in pipes entails both a loss 
of pressure and a loss of power. 

93. Loss of pressure or head is the difference of pressure in the 
air between the in-take and the discharge end of the pipe line. 
This loss as has been mentioned is due : 

1. To pressure consumed in causing the air to flow from one 
end of the pipe line to the other. It is as explained, not a loss, 
strictly speaking. 

2. To pressure consumed in overcoming friction and increasing 
the velocity. This loss is unavoidable but can be minimized by 
intelligent design of the pipe line. 

3. To leakage which causes the air remaining in the pipe to 
expand and therefore lose pressure. This loss is avoidable and 
in a well-constructed pipe line should be practically nil. 

4. To difference in elevation between the compressor room and 
the points of use. (See Article 97.) 

94. Loss of Power. — The ultimate loss of power which is 
chargeable to transmission, is the difference between the amount 
of power, residing in the compressed air when it enters the pipe 
line and that which is available at the discharge end of the pipe 
line. (See also Articles 97 and 102.) 

Since the amount of work required to compress air and the 
amount of work which compressed air is capable of performing, 
depends on pressure as well as on volume and since loss of pres- 
sure increases the volume (the temperature remaining the same), 
it follows that the loss of power is not in direct proportion to the 
decrease in pressure but is partly compensated by the resultant 
increase in volume. 

For instance, if air enters a pipe at 100 lb. and is discharged 
at 80 lb. gage, there is a loss in pressure of 20 per cent. From 
equation (1), Article 110 the theoretical work which 1 cu. ft. of 



TRANSMISSION OF COMPRESSED AIR 87 

compressed air is capable of performing in expanding adiabatic- 
ally from 100 lb. gage to atmospheric pressure is 25,740 ft.-lb. 
This represents the potential energy of 1 cu. ft. of air when it 
enters the pipe line at 100 lb. gage. This cubic foot of com- 
pressed air when its pressure is reduced to 80 lb. at the end of the 
pipe line has expanded into a volume of 1.211 cu. ft., which at a 
pressure of 80 lb. is capable of doing work to the amount of 
24,000 ft.-lb. Hence the loss of power in this case amounts to 
only 7 per cent, as against a pressure loss of 20 per cent. 

Loss of pressure in air transmission must therefore not be con- 
founded with loss of power. Both losses in a well-proportioned 
pipe line are usually small compared with other losses in the 
production and use of compressed air, such as result, for instance, 
from the heat produced during compression which is subsequently 
lost in transmission. 



CHAPTER XI 

DIMENSIONS OF PIPE-LINES FOR CONVEYING COMPRESSED 

AIR 

95. From what has been said, it is evident that no uniform 
rule can be followed in deciding on the proper dimensions of 
pipes for air transmission. Almost any degree of transmission 
efficiency can be obtained by using pipes of large diameter. This, 
however, may result in extravagant first cost. On the other hand, 
an unwise economy in first expenditure may reduce the efficiency 
of the whole system to a point where the cost of operation will 
more than offset the original saving in cost of installation. 

A proper design of pipe line must therefore take into considera- 
tion not only first cost of pipe and interest thereon but also the 
subsequent operating costs. The latter will vary with the size 
of the compressor, the pipe line, and with local conditions such 
as cost of transportation, fuel, labor, etc., in the part of the country 
where the plant is to be erected. The problem must be solved 
for each individual installation. 

In order to make comparisons, however, we must have means 
of calculating, at least approximately, the minimum dimensions 
of a pipe which will fill the requirements of a certain installation. 
Or, if the size of the pipe is given, we must be able to calculate 
the work which the compressor must perform in order that the 
available power at the discharge end of the pipe line will be a 
certain quantity. Or, if a certain compressor and pipe line are 
on hand, we must be able to calculate the power that will be 
available at the discharge end of the pipe line before we buy and 
install our air engines. 

The conditions that affect pressure, volume, density, tem- 
perature, velocity and friction of the air passing through a pipe 
line, are so numerous that the formulas proposed by authorities 
cannot be expected to give more than safe approximate results 
for pipe line dimensions. Such results should be considered 
the maxima or minima in each case and ample allowances should 
be made for undetermined contingencies. 

The formulas selected for this treatise are those proposed by 
Johnson-Rix. 

88 



PIPE-LINES FOR CONVEYING COMPRESSED AIR 89 

96. Formulas for Pipe Line Computations. — 

Let Pi and P% = absolute pressures at intake and discharge 
terminals of pipe, in pounds per square 
inch. 

V = volume of free-air equivalent in cubic 
feet per minute, passing through pipe. 

L = length of pipe line in feet. 

D = diameter of pipe in inches. 

Then ft.-ft.-^ (1) 



D-4 



V 2 L 



2000(Pi 2 -P 2 2 ) 



12) 



v= ^m^-pv (3) 

_ 2000Z) 5 (Pi 2 -P 2 2 ) 
L y 2 (4; 



/ V 2 L 



2000D' 



<JpJ- 



V 2 L 



2000Z) £ 



(6) 



Example 1. — What should be the diameter of a pipe line, 1200 ft. 
long that will transmit the equivalent of 4000 cu. ft. of free air per 
minute with a pressure loss of not more than 8 lb. Initial pressure = 
100 lb. gage. Atmospheric pressure = 14.7 lb. 



t? *• /m n 1 4000 2 X1200 

From equation (2) D= y 



2000(1 14.7 2 -106.7 2 ) 
whence D = 5.58, say 6 in. 

Example 2. — What is the free air equivalent in cu. ft. per minute that 
can be transmitted through an 8-in. pipe line 11,000 ft. long so that 
the pressure loss is not more than 5 lb. Initial pressure = 80 lb. 
gage. Atmospheric pressure at locality selected = 12.02 lb. 



v + - ,«x T7 j2000X8 6 (92.02 2 -87.02 2 ) 
Irorn equation (3) \ = yj ^j^ '- 

whence V = 2300 cu. ft. of free air per min. 

Example 3. — What must be the initial pressure of an equivalent 
of 500 cu. ft. of free air per minute so that at the end of a 2-in. pipe line, 



90 COMPRESSED AIR 

300 ft. long it has a pressure of 80 lb. gage. Atmospheric pressure at 
locality selected = 11.30 lb. 






From equation (5) Pi=\^ 



/500 2 X300 
2000 X 2 s 



whence Pi = 97.5 lb. absolute 
= 86.2 lb. gage 

Example 4. — What will be the terminal pressure of an equivalent 
of 500 cu. ft. of free air per minute at the discharge end of a 5-in. pipe 
line, 2500 ft. long, when initial pressure = 90 lb. gage. Atmospheric 
pressure at locality selected = 12.02 lb. 



From equation (6) P 2 = V 102 - 022 "^^^ 

whence P 2 = 101.02 lb. absolute 
= 89 lb. gage 

Example 5. — What is the permissible length of a 6-in. pipe line that 
will transmit the equivalent of 2000 cu. ft. of free air per minute with a 
pressure loss of not more than 10 lb. Initial pressure = 90 lb. gage. 
Atmospheric pressure = 14.7 lb. 

,. , A . T 2000X6 5 (104.7 2 -94.7 2 ) 
From equation (4) L = ^qoO 2 

whence L = 7750 ft. 

97. Effect of Altitude on the Transmission of Compressed 
Air. — The formulas given under Article 96 do not take into 
consideration any difference of elevation between the in-take and 
the discharge end of the pipe line, but assume that the two ter- 
minals of the pipe line are practically at the same elevation. In 
compressed-air installation, it happens frequently that the engines 
using the compressed air are located at a considerable elevation 
above the compressor in which case proper allowance must be 
made for the loss of pressure due to this fact. 

Example. — At a mine located 1500 ft. above the compressor house, 
a free air equivalent of 4000 cu. ft. per minute is required at a gage 
pressure of 80 lb. The length of the pipe line is 2600 ft. Elevation at 
compressor is 3000 ft. above sea level. 

(a) If a loss of 6 lb. is allowed for pipe friction, what must be the gage 
pressure of the air when leaving the compressor? 

(6) What should be the diameter of the pipe? 



PIPE-LINES FOR CONVEYING COMPRESSED AIR 91 

Solution (a) From Table VI atmosph. press, at compressor = 13.16 lb. 
From equation (4), Art. 4, atmosph. press, at mine 

logP 450 o = log 13.16 — 122 4+461) (assuming temp. = 60°F.) 

Whence P 45 oo= 12.32 lb. 

Hence, absolute pressure of compressed air at mine 

P 2 = 80+12.32 = 92.32 lb. abs. at discharge terminal of pipe line. 

The corresponding pressure at the intake of the pipe is found from the 
same formula: 

1O ^ 1 ' = ^ 92 - 32 + 122.4( 1 60°+461) 
Whence Pi 1 = 98.65 lb. absolute. 

Adding to this the 6 lb. allowed for pipe friction, it follows that the 
compressed air leaving the compressor must have a pressure of 

P 2 =104.65 abs. or 104.65-13.16 = 91.49 lb. gage 

in order that the pressure at the mine may be 80 lb. gage. Obviously 
on account of difference in altitude alone, an extra pressure of 98.65 — 
92.32 = 6.33 lb. is required. 

Solution (b). Introducing the respective values in equation (2), 
Art. 96, we get diameter of pipe 



=v; 



;) . , 4000 2 X2600 



2000(104.65 2 -98.65 2 ) 
Whence D = 6 in. 

98. Dimensions of Branch Pipes. — In selecting the dimensions 
for branch pipes to carry compressed air, it must be borne in 
mind that the carrying capacity of a pipe is not directly pro- 
portional to the cross-section of the pipe. Under the same con- 
ditions of length and head a 3-in. pipe, for instance, will carry 
only 16 per cent, of the volume which a 6-in. pipe can carry. 
Therefore if a 6-in. main is to be divided into two branches, two 
3-in. pipes would not do the work, neither would the combined 
capacities of a 4- and 5-in. pipe be sufficient. This will be seen 
from Table IX. 

Going to the column showing the capacities for a 6-in. pipe 
and following this column down to the figure opposite 4 in., we 
find that the capacity of a 4-in. pipe is only 35 per cent, of the 
capacity of a 6-in. pipe and for the 5-in. pipe we find it to be 
63 per cent, of the 6-in. pipe capacity. The sum of the 4- and 5- 
in. pipe capacities is therefore only 98 per cent, of the 6-in. pipe 
capacity, resulting in a slight additional friction from the point 



92 COMPRESSED AIR 

of diversion of the branches. If the branches were made of 4 1/2- 
and 5-in. pipes, the percentages would be 47 and 63 respectively, 
their sum 110 per cent., resulting in a slight decrease of friction 
and therefore an easier flow beyond the diversion of the branches. 

99. Effects of Elbows and Bends on the Flow of Air in 
Pipes. — Bends and elbows in a pipe line have the effect of in- 
creasing the friction of the air and thus reduce the pressure. 
In table below which is taken from the Trade Catalogue of the 
Nor walk Iron Works Co., is given the length of pipe in terms of 
diameters which will produce the same frictional effect as an 
elbow having a certain radius. 

For instance, the frictional resistance in a 6-in. pipe line 500 

ft. long containing five elbows with a radius of 18 in. or three 

diameters each, would be the same as that produced by a straight 

• r *™ , 5X8.24X6 
pipe line 500 H r^ = 520 ft. long. 

From the table the beneficial effect of a gradual curve in 
comparison with a short sharp turn, is quite evident. 

Radius of elbow 5 diameters. Equivalent length of straight pipe 

7.85 diameters. 
Radius of elbow 3 diameters. Equivalent length of straight pipe 

8.24 diameters. 
Radius of elbow 2 diameters. Equivalent length of straight pipe 

9.03 diameters. 
Radius of elbow 1 1/2 diameters. Equivalent length of straight pipe 

10.36 diameters. 
Radius of elbow 1 1/4 diameters. Equivalent length of straight pipe 

12.72 diameters. 
Radius of elbow 1 diameter. Equivalent length of straight pipe 

17.51 diameters. 
Radius of elbow 3/4 diameter. Equivalent length of straight pipe 

35.09 diameters. 
Radius of elbow 1/2 diameter. Equivalent length of straight pipe 

121.20 diameters. 

100. Velocity of Compressed Air Flowing Through a Pipe 
Line. — 

Let Y c = volume of compressed air in cubic feet per 

minute. 

v = velocity in feet per minute. 

A = area of pipe section in square feet. 

y 
then v = -j- ft. per minute. (1) 



PIPE-LINE EFFICIENCY 93 

If in Example (2), Art. 96, the average pressure of the air is 

. 92.02+8 7.02 QQ _ 
taken as ~ = 89.52 lb. abs. 

_ 7 C 12.02 _ T/ 2300X12.02 otn 

Then T = 89^2 WhenCe Vc== 89.52 = 31 ° CU ' ft ' 

The sectional area of an 8-in. pipe is 0.35 sq. ft. 

310 
Hence z; = p-^-r = 885 ft. per min. or 14.8 ft. per second. 

Although pressure losses in a pipe line are obviously a function 
of the volume of air transmitted per minute and therefore of 
velocity, as well as of the length, the diameter and roughness 
of the pipe line, the individual effect of these factors has not as 
yet been definitely determined. It is generally conceded, 
however, that for economical transmission the actual velocity of 
the air in a line constructed for long continuous operation should 
not materially exceed 30 ft. per second. If either the diameter 
of the pipe or the volume of the air to be transmitted are fixed, 
the velocity is decreased in the first case by limiting the volume 
of air, and in the second case by increasing the diameter of 
the pipe. 

100A. The Planning of a Transmission Line. — It has been 
shown that the transmission of compressed air involves numerous 
losses depending on the size, length and roughness of the pipe, 
on the number of bends and elbows, on the volume of air to be 
transmitted and the initial pressure with which it enters the pipe 
line. 

The intelligent planning of the pipe line should therefore 
aim to minimize these losses as much as practicable by trans- 
mitting the air to the points of use over the shortest possible 
route, requiring the least number of elbows, joints and other 
obstructions, and by selecting this route so that the pipe is access- 
ible at all points. This is desirable to permit frequent inspection 
and stoppage of leaks which, as a rule, are the chief cause of 
extreme pressure losses. 

It usually pays to do a certain amount of grading and excavat- 
ing in order to eliminate sudden changes in both the horizontal 
and vertical alignments of the pipe line. 

If air is to be transmitted through a network of pipes, not 



94 COMPRESSED AIR 

only the diameter of the air-main but the diameters of all the 
branch pipes should be calculated with the highest degree of 
accuracy. 

This is accomplished by applying the formulas in Art. 96 to 
both types of pipes. 

Example. — A compressor furnishes to a mine air that has a pressure 
of 100 lb. absolute at the intake terminal of a 6-in. air main. The free- 
air equivalent is 3000 cu. ft. per min. At a point, 2600 ft. from the 
compressor (measured along the pipe line) a 1200-ft. branch line is 
to be taken off to supply air at 87 lb. absolute to six stoi ing drills, 
whose combined free-air consumption is 300 cu. ft. per min. What 
should be the diameter of the branch pipe? 

For the solution of this problem it is necessary to know the normal 
air pressure at the point of take-off. In an existing pipe line the pressure 
may be obtained by attaching a pressure gage to the air main at that 
point. But if the branch pipes are to be planned simultaneously with 
the main pipe, the expected pressure at the point of take-off must be 
calculated by equation (6) Art. 96. 



\ * 200 



2 L 



2000Z) 5 



The minimum diameter of the branch pipe will be from equation (2), 
Art. 96 

>2000(P*-P*) 

D JI 30PX1200 in> 

^2000(92 2 -87 2 ) 

A pipe smaller than that would supply neither the required quantity 
of air nor the required pressure. 



PIPE-LINE EFFICIENCY 

101. The efficiency of a pipe line is the ratio between the 
available energy for doing useful work residing in the air at the 
discharge end, and that which is available at the in-take end of the 
line. 1 In computing this ratio the temperature of the compressed 
air must be assumed to be the same at both terminals of the pipe 
line. For, whatever the dimensions of the pipe, the compressed 

1 See also Article 102. 



PIPE-LINE EFFICIENCY 95 

air at the discharge end will be practically at outside temperature, 
that is, at the temperature of the free air taken into the com- 
pressor cylinder. Any extra heat left in the compressed air 
when it enters the pipe line should be charged to the efficiency 
or rather the inefficiency of the cooling devices of the compressor 
and the receiver, and not to the efficiency of the pipe line. 

The maximum energy for doing useful work in expanding 
isothermally down to atmospheric pressure, which resides in a 
given weight of compressed air occupying a volume V 2 , is the 
same as the energy expended in compressing isothermally that 
same weight of free air to a given pressure and delivering it under 
that pressure via the receiver into the pipe line. 

Let Vi = volume in cubic feet of a given weight of free air to be 
compressed, being at outside temperature. 

Pi = initial absolute pressure in pounds per square inch. 

P 2 = final absolute pressure in pounds per square inch. 

Vi = volume in cubic feet of the same weight of air after 
being compressed isothermally to a pressure P 2 . 

Then the energy residing in this volume Yi of compressed air 
after leaving the compressor and at the entrance of the pipe 
line is: 

Energy at entrance of pipe line = 144 P1V1 log e ^ 

P 2 
= 144 PiVi log e w foot-pounds. 

At the end of the pipe line this volume V2 owing to the loss 
of pressure due to friction and other causes, has expanded into a 
volume 7 3 , whereas the pressure has decreased to a pressure P 3 . 

The energy residing in this volume F 3 at a pressure P 3 for doing 
useful work is the same as the energy that would have been 
expended in compressing isothermally a volume Vi of free air 
from a pressure Pi to a pressure P3 and delivering the compressed 
air which now occupies a volume F 3 via the receiver into the pipe 
line. 

That is, energy residing in the compressed air at the end of the 
pipe line: 

W n = 144 Pi7i loge y l = 144 P X V i \og e y foot-pounds. 



96 COMPRESSED AIR 

Hence efficiency of pipe line 

144 P^ log 



E 



Pi 



144 P^ log, 
and since the modulus cancels 



Pi 



1 p s 

£=— -y a) 

log ft 

As P 3 is always smaller than P 2 it would appear from formula 
(1) that the efficiency of a pipe line of certain dimensions becomes 
smaller, the higher the pressure P 2 is at which the compressed air 
enters the pipe line. This would be true if P 3 remained the same 
when P 2 is being increased. 

According to equation (6), Art. 96, however, the terminal 
pressure and therefore the potential energy of the air at the 
discharge end of the pipe line increases with the increase of 
the initial pressure, and so does the pipe line efficiency. 

The subsequent loss of energy due to the fact that the ex- 
pansion of the compressed air in the air engine will be adiabatic 
instead of isothermal, must be charged to the efficiency of the 
air engine or to the whole system, but not to the pipe line. 

Example. — What is the efficiency of a 6-in. pipe line, 1200 ft. long, 
delivering at its terminal a free-air equivalent of 4000 cu. ft. per minute 
at a pressure of 92 lb. gage? Atmospheric pressure = 14.7 lb. 

Introducing in equation (5), Art. 96, the proper subscripts, the re- 
quired initial pressure will be 



•.=v 



««"XlM0 +m7! , nMlb ., ta . 



2000 X6 5 
P 3 106.7 

Then pruj =7 - 2Q 

, P 2 112.34 

and P~riAj~ = 

Whence E = }° g ^ = 0.975 or 98 per cent, 

log 7.64 ^ 

The pressure loss in this case is 112.34 — 106.70 = 5.64 lb. 

If the same quantity of air were transmitted through the same pipe 



PIPE-LINE EFFICIENCY 97 

line with an initial pressure of 130 lb. abs. the end pressure according to 
equation (6), Art. 96, would be: 



showing a pressure loss of only 130.0 — 125.5 = 4.50 lb. 

This indicates that, other things remaining the same, higher initial 
pressures result in higher pipe line efficiency. 

101 A. Resume of Pipe Line Computations. — As has been pointed out, one 
of the chief difficulties of accurate pipe calculation lies in the fact that com- 
pressed air, while flowing through a pipe, creates friction which gradually 
but persistently decreases the pressure of the air. This loss of pressure is 
accompanied by a corresponding expansion of the air, that is, by an increase 
in volume. To transmit this increased volume through the pipe, requires 
increased velocity of flow resulting in a further increase of friction loss 
and so on. 

Mathematical formulas for general use must of necessity assume more or 
less uniform conditions. In the pipe line formulas it is assumed that fric- 
tion losses are directly proportional to the length of the pipe. That is, if a 
loss of 8 lb. occurs, for instance, in a pipe 5.85 in. in diameter and 1200 ft. 
long, transmitting a free-air equivalent of 4000 cu. ft. per min. (Example 1, 
Art. 96), then a loss of 16 lb. would be found from the formulas for a 2400 
ft. pipe line of the same diameter and transmitting the same amount of air 
at the same initial pressure. 

The assumption implies that the velocity of flow is the same at all points 
in the line, which would only be the case if the pipe line were constructed 
with a gradually increasing cross-sectional area, corresponding to the in- 
crease in volume mentioned above. This is, of course, impracticable in 
commercial operations. 

Although the pressure loss due to friction increases with the length of the 
pipe, the number of elbows and other obstructions, the actual loss in any 
particular section of the pipe line is greater than that in the preceding one, 
not in direct proportion to the length of the pipe but in a proportion that 
eludes statement by simple mathematical formulas. The shorter the pipe 
line, the more nearly correct will be the results obtained from the formulas, 
because the more nearly uniform will be the conditions between the intake 
and the discharge terminal of the pipe line. The longer the pipe line, the 
greater will be the discrepancies between the results obtained by the form- 
ulas and those obtained in practice. Hence the necessity of making suffi- 
cient allowance for the many incalculable factors such as, for instance, the 
roughness of the pipe and the obstructions the air meets at each joint of the 
pipe line. Unsatisfactory results in long transmission lines are frequently 
due to failure to realize the magnitude of the pressure losses caused by these 
factors. 

No general rule can be laid down as to the proper allowances to be made 
in each individual case. All that may be said is, that it usually pays to in- 
crease the diameter of the pipe beyond that obtained by calculation up to a 
point at which the economic advantages gained no longer balance the extra 
cost of installation. 






98 COMPRESSED AIR 

102. Effect of Altitude on Pipe -line Efficiency. — In making 
estimates of pipe-line efficiency it must be borne in mind that so- 
called losses, due to difference of elevation, as explained under 
Article 97 cannot be charged to the efficiency of the pipe line. 
For the pressure loss, due to the difference of elevation is a con- 
stant quantity, no matter what the dimensions of the pipe line 
may be. This loss must be charged to the compressed-air instal- 
lation as a whole as pointed out in Article 121. 

103. Final Dimensions of Pipe Line. — In any individual instal- 
lation, the length of the pipe line is generally a given quantity 
as well as the amount of air that must be delivered at a certain 
pressure at the end of it. We have seen that high initial pressures 
give high pipe-line efficiency, but require more powerful and 
more expensive compressors. On the other hand, with low initial 
pressure, a more expensive pipe line of larger diameter is required 
in order that the pressure at the discharge end may be a definite 
quantity. 

Since the power residing in compressed air depends on the pres- 
sure as well as on the volume, and since in a pipe line the decrease 
in pressure is, up to a certain point, greater than the loss of power, 
it is a question whether it is more economical to have a high initial 
pressure and a smaller pipe line or a lower initial pressure and a 
larger pipe line. 

In general,, the decision in favor of the one or the other must be 
made by taking into consideration a number of factors and by 
comparing the costs for each individual case. 

In making these computations it must also be borne in mind 
that the power required to compress air to a certain pressure is 
not in direct proportions to these pressures themselves as pointed 
out under Article 49. 

Under certain conditions it may be more economical in the end 
to have high initial pressures with a smaller size pipe line. Under 
other conditions the reverse may be the case. This is a problem 
which can be only solved after due consideration of all the condi- 
tions which affect the plant to be installed, such as cost of pipes, 
cost of fuel, transportation, labor, etc., and the probable life of 
the plant. 

104. Pipe-line Construction. — From what has been said re- 
garding losses in the transmission of compressed air through 
pipes, it is evident that not only the design of a pipe line should 



PIPE-LINE CONSTRUCTION 99 

be given due attention, but that the laying of the line should 
also receive considerable care. 

Friction being the chief cause of loss in an otherwise well- 
proportioned and constructed pipe line, it is desirable that the in- 
terior of the pipe should be as smooth as possible. In ordering 
pipes, particular mention should be made that the interior of the 
pipes should be free from all roughness such as scale, blisters, 
lumps, etc., and when the piping is put up, great care should be 
taken to clean the lengths thoroughly of dirt which may have 
gotten into them. 

Where the line is exposed to severe cold, the moisture in the 
air will condense and the water so formed will freeze in the pipes 
until it throttles or chokes the pipe altogether. Since this takes 
place particularly in low points of the pipe line which form pockets 
for the accumulation of the entrained water, such pockets should 
be avoided as much as possible. 

Valves and bends will increase the friction to a great extent. 
A globe valve causes the greatest loss and an ell or tee causes a 
loss of one-half to two-thirds that of a globe valve. Consequently 
care should be taken that gate valves be used instead of globe 
valves, and as few bends put in as possible. Where turns are 
absolutely necessary they should be made with as long a sweep as 
possible, either by bending the pipe without kinking it or by 
using long-sweep ells or tees. 

Long pipe lines which are exposed to high temperatures should 
be provided with expansion joints to avoid springing leaks. 
Leaks should be attended to as soon as discovered. They cause 
the air in the pipes to expand and to lose pressure rapidly. 

The heavy losses, caused by leaks in a pipe line will become 
clear by a study of Article 105 and the numerical example con- 
tained therein. 

FLOW OF COMPRESSED AIR FROM AN ORIFICE INTO THE 
ATMOSPHERE 

105. Let the confined air be under a pressure of "p" pounds 
gage. The theoretical velocity with which it flows from an 
orifice into the atmosphere is : 

v = ^l2gh feet per second. (1) 

in which v = velocity in feet per second. 

g = acceleration due to gravity = 32.2 ft. per second. 



100 COMPRESSED AIR 

h = height in feet of a column of air of uniform density, 
corresponding to a gage pressure p and exerting 
a pressure of p pounds, on its base which is assumed 
to be 1 sq. in. in area. 
The volume V of this column is : 

V=—-h cubic feet. (2) 

144 v ' 

It is evident that the mass of air forming this column must 
weigh p pounds in order to exert a pressure of p pounds per square 
inch which is the area of its base. 

According to Article 2 the weight W of 1 cu. ft. of atmospheric 
air at 60° Fahr. is 0.0764 lb. The weight W i of 1 cu. ft. of air 
having a density corresponding to a gage pressure p, we find from 
Article 22: 

Wi p+U.7 
W 14.7 
whence 

Wi = 0.0764 V \l^' 7 lb. per cubic foot. 

Since the total weight of the air column must be p pounds, its 
volume must be: 

V = — 1 * a * cubic feet. /D \ 

0.07642^ (3) 

Combining equations (2) and (3), we have: 

Ji p 

l44 _ z>+14.7 

0.0764 P1 



whence 



14.7 
144pXl4.7 



0.0764(p+14.7) 



^ = 27,707^^- (4) 

Introducing this value in equation (1) we get: 



w 



2X32.2X27,707^^ 



FLOW OF COMPRESSED AIR THROUGH AN ORIFICE 101 



or, theoretical velocity v = 1336.*/ *j — feet per second (5) 

The actual velocity is, of course, less owing to friction and other 
causes. It is obtained by multiplying the theoretical velocity 
by an orifice coefficient "c." For ordinary compressed air 
problems such as leaks in receivers and pipe lines, where the 
pressures range from five to ten atmospheres, this coefficient 
may be taken as 

c = 0.50 



This gives for actual velocity: 

v = 1336X0.50 



4 



p+14.7 



or = 668 A / — -^-— feet per second. (6) 

\p+14.7 

The volume Vi of compressed air in cubic feet per minute, 
that flows from an orifice of the area "a" square feet is: 

Fi = 60XaXv = 60X668XaJ— -2— - 

\ p+14.7 



or Vi= 40,080 Xcu / — , \. . „ cu. ft. of compressed air per min. (7) 
\p+14.7 

After expansion to atmospheric or free air, and after having 
assumed outside temperature, the volume Vi of compressed air 
will occupy a volume V a which we find from Article 15 as follows: 

Ys- P 2 

vrp„ 

p 
whence V a =Vi^- (8) 

•to 

in which P a = atmospheric pressure in pounds per square inch 
= 14.7. 
Pi = absolute pressure of compressed air in pounds 
per square inch = p+14.7. 
Introducing values in equation (8) we get : 

40,080(p + 14.7) 



V a = 



14.7 \p+ 



a \p+ 14 J 



or V a = 2727 a Vp(p+ 14.7) cubic feet (9) 

of free air per minute at outside temperature. 



102 COMPRESSED AIR 

in which a = area of orifice in square feet. 

p — gage pressure of compressed air in pounds per 
square inch. 

Example. — Air under pressure of 80 lb. gage escapes from various 
leaks in a pipe line. What is the quantity of escaping air, expressed 
in cubic feet of free air per minute, when the combined area of the 
leaks is 1/2 sq. in.? 
In this case 

0.50 .. 
a=-jjf sq.ft. 

2727 YO ^0 

Therefore V a = ^ V80(80+14.7) =824 cu. ft. 

of free air per minute, having outside or in-take temperature. 

If the compressor is built to furnish 1500 cu. ft. of free air per 
minute, the leaks in the pipe line will cut down its useful capacity to 
less than one-half, without, however, cutting down the power required 
to run it. 

The theoretical horse-power required to compress in two stages 824 
cu. ft. of free air per minute to 80 lb. gage and deliver it into the 
receiver, is (from column 7, Table V) 

824X0.141 = 116 h.p. 

which represents the theoretical power loss, due to the leaks, which at 
first sight seem rather insignificant. This points to the importance of 
stopping them as soon as discovered. 



PART III 

THE USE OF COMPRESSED AIR 



CHAPTER XII 
THEORY OF AIR ENGINES 

106. Compressed air can be used to operate an engine in a 
manner similar to steam, either at full pressure or expansively. 
In the first case air at full pressure is admitted into the cylinder of 
the engine during the entire stroke and is exhausted practically 
at full pressure. In the second case air is admitted into the 
cylinder during part of the stroke, is then cut off and used ex- 
pansively for the remainder of the stroke. In practice it is 
always exhausted at a pressure slightly above atmospheric pres- 
sure for reasons stated in Article 112. 

107. Compressed Air Used at Full Pressure During the Entire 
Stroke. — Although the efficiency of an engine using air in this 
fashion is, of necessity, small, the waste of energy in such engines 
is usually compensated in part by the saving in first cost and 
labor, due to the simplicity of construction of such machines and 
the ease of handling them. 

108. The theoretical net work in foot-pounds performed per 
stroke by engines using air at full pressure during the entire 
stroke is equal to the total force multiplied by the distance 
through which it acts. 

The total force is: (absolute pressure of compressed air on the 
in-take side minus atmospheric pressure on the exhaust side) 
multiplied by (area of piston) . The distance through which the 
force acts is the length of the stroke. 

Let W n = net work in foot-pounds. 

Pi = absolute pressure of air in pounds per square inch on 

in-take side. 
P a = atmospheric pressure in pounds per square inch on 

exhaust side. 
A = area of piston in square feet. 
L = length of stroke in feet. 
Vi = volume of compressed air in cubic feet taken into the 

cylinder per stroke. 

105 



108 COMPRESSED AIR 

Then W n = 144 (Pi-P )XAL 

And since AL = Vi 

W n = 144 (Pi -PaWi foot-pounds. 

Assume that the volume V\ of air required to do this work is 

obtained by isothermal compression, then the work of supplying 

this volume would be a minimum, viz: 

P x 
144 P a V a log e p- foot-pounds 

in which V a = volume of free air which, after being compressed 
isothermally to an absolute pressure Pi would occupy a volume Vi 

Therefore V a = V^ 

109. Maximum efficiency of air engine using air at full pressure 
during the entire stroke is: 

E _ 144 (Pl-Pq) Vl _ Pl-Pq 

144P.7i§log.J* Piloge^ 
Dividing dividend and divisor by P a 

P 

E -Pl. Pi 

K l0S 'K 

This shows that the higher the initial pressure Pi at which the 
air enters the air engine, the smaller becomes the efficiency. 

Example. — A striking example of an apparatus using air at full pres- 
sure during the entire stroke is the well-known rock drill. In consump- 
tion of power it is one of the most wasteful machines, but from a prac- 
tical point of view its efficiency stands at present unquestioned. 

The theoretical efficiency of a rock drill with a cylinder of 3 1/4 in. in 
diameter, 6 3/4-in. stroke, 400 strokes per minute, using air at 60 lb. 
gage is as follows: 

Area of piston 8.29 sq. in. 

Piston displacement 8.29X6 3/4= 55.96 cu. in. ' 

Volume of air taken into cylinder per minute 

EK Oft 

^1^X400= 12.95 cu. ft. at 60 lb. 

17 2io 

Volume of free air, equivalent to 12.95 cu ft. at 60 lb. 

V a = 12.95 6 ° ] ^ 1 y ,7 = 65.8 cu. ft. per min. 



THEORY OF AIR ENGINES 

Theoretical horse-power required to compress 
and deliver 65.8 cu. ft. per min. at 60 lb. gage 

(from column 4, Table V) 65.8X0.134= 8.8 h.p. 

Power utilized in striking rock (forward stroke 
.6 3/4X200 



107 



only), 8.29X60X 



12 



56,200 ft.-lb. 



= 1.70 h.p. 
In this case the theoretical efficiency of the drill is only 19 per cent. 
The practical efficiency will be much less, due to friction leakage, etc., 
in the drill itself and to power losses in bringing the air to the drill. 

COMPRESSED AIR USED WITH COMPLETE ADIABATIC 
EXPANSION 

110. The theoretical net work performed per stroke by engines 
using air with complete adiabatic expansion down to atmospheric 
pressure, is deduced in the same manner as that for compression. 




Fig. 15. 



Referring to Fig. 15: 

W n = 144 X (shaded area ABCD) foot-pounds 
But area ABCD = area ABFE 
plus area FBCG 
minus area EDCG 
Area ABFE = P 2 V 2 



Area FBCG 



= \PdV 



108 




COMPRESSED AIR 


But 


PV n 


D T7 n R ^2^2 


hence area FBCG 












rv a 






-w f 






e/F 2 






r 7a 






= P 2 W 1 yW 






Jf 2 






=^T 2 I _— 


' 




p 2 TV7 a 1 ~ n -p 2 y 2 r T 2 1 ~ n 




1-n 


and since 


P 2 IY 


= Pa7a" 


we can write : 




area FBCG 




PaFa n ya 1 '" n -P27 2 n 7 2 1 - n 


1-n 






P.7.-PlF« 






1-n 






P2V 2 -P a V a 






n-1 


area EDCG 




= PaV a 


therefore 


w* 


= iu(p 2 v 2 + P2V ^ P 1 aVa 

-n-l Pi7i L 1 ~P 2 7 2 J 



P«F a ) 



and since Tr = \p/ 



144 n 
^n= n - T P 2 7 2 



[>-©*! 



foot-pounds. (1) 



THEORY OF AIR ENGINES 109 

in which W n = net work in foot pounds per stroke. 

P 2 = absolute pressure in pounds per square 

inch of compressed air entering cylinder. 
V2 = volume of compressed air in cubic feet 

taken into the cylinder per stroke. 
P a = atmospheric pressure in pounds per square 
inch. 
n= 1.406. 

111. The theoretical horse-power which a volume 7 2 of air 
in cubic feet per minute, compressed to an absolute pressure P 2 
is capable of developing during admission and adiabatic ex- 
pansion to atmospheric pressure, is obtained by letting V 2 in 
the formula for W n represent the number of cubic feet per minute 
admitted into the cylinder and by dividing the whole by 33,000. 

Theoretical horse-power = 33 "oo^-l) [ X ~ (ft) " ] (1) 

in which P 2 = absolute pressure in pounds per square inch of air 
entering cylinder. 
V2 = volume of compressed air taken into the cylinder 

in cubic feet per minute. 
P a = atmospheric pressure in pounds per square inch. 
n = 1.406. 

112. In practice complete expansion to atmospheric pressure 
is not feasible for the following reasons: 

1. The resulting increase in volume of the expanded air would 
require a more expensive engine with larger cylinders than is 
warranted by the small gain in power. 

2. To overcome the friction of the engine near the end of the 
stroke and to cause the air to properly exhaust against the back 
pressure of the atmosphere, the pressure of the exhaust air must 
be somewhat greater than the atmospheric pressure. 

3. Unless the compressed air is reheated before being used, its 
temperature when entering the air cylinder of the engine is that 
of the surrounding atmosphere. A high ratio of expansion will 
result in very low final temperature and quite often in freezing 
of the moisture in the air around the exhaust ports. 

Example. — Assuming that air at 80 lb. gage and 60° Fahr. enters the 
cylinder of an air engine and that it is allowed to expand adiabatically 



110 



COMPRESSED AIR 



to atmospheric pressure at sea level, then the theoretical final absolute 
temperature of the exhaust air would be: 



n-l 0-29 

r 1= r(^) " =(60+461) (i|y) =305° absolute. 

= -156°Fahr. 

COMPRESSED AIR USED WITH PARTIAL ADIABATIC EXPANSION 

113. For reasons stated in Article 112, air engines usually 
work with partial expansion, that is, a volume of compressed air 
is admitted during part of the stroke, is then cut off and allowed 
to expand down to a pressure somewhat above atmospheric 
pressure. 




Fig. 16. 

Referring to Fig. 16 the net work performed during one stroke 
of the piston is: 

W n = 144 X (shaded area ABHKD) 
But area ABHKD = area EABF=P 2 V 2 

plus area FBHM= P2V2 ~^ lVl 

minus area DEMK = P a Vi 
P2V 2 -P 1 V 1 



whence W n = 144 (P 2 V 2 -\ 



n-l 



—P a Vi) foot-pounds, (1) 



in which P 2 = initial absolute pressure in pounds per square 
inch of air entering engine. 



THEORY OF AIR ENGINES 111 

V 2 = volume of compressed air in cubic feet taken into 
the cylinder per stroke. 

Pi = absolute pressure in pounds per square inch of 
exhaust air. 

Vi = volume of air exhausted per stroke at a pres- 
sure Pi. 

P a = atmospheric pressure in pounds per square inch. 
n = 1.406. 

114. Mean gage pressure of air during admission and partial 
adiabatic expansion: 



p _ Wn 

JT m. — 



144 Fi 






Pi^-Pi 



Vi n-l 



pounds per square inch. 



115. Theoretical horse-power which a volume of compressed 
air per minute is capable of developing during admission and 
partial adiabatic expansion: 

144 r , P 2 F 2 -P i7i T/ "I 
Horse-power= 33^ \P 2 V,+—^- l P a 7ij 

in which, P 2 = absolute pressure in pounds per square inch of 
in-take air. 

V 2 = volume of compressed air in cubic feet taken into 
the cylinder per minute. 

Pi = absolute pressure in pounds per square inch of ex- 
haust air. 

Vi = volume of air exhausted at a pressure Pi in cubic 
feet per minute. 

P a = atmospheric pressure in pounds per square inch. 
n = 1.406. 

In practical problems P 2 , V2 and P a are always known, and 
either Pi or Vi are given. 

If Pi is given, then Vi is found from the relation: 

V x /P 2 \n 



V 2 \Pj 



l_ 

whence Vi = V 2 1~) 



112 COMPRESSED AIR 

If Vi is given, as in engines having a certain cut-off, then Pi 
is found from the relation: 



whence 



Pi- (La 

p 2 ~\vJj 



Example. — Find theoretical horse-power developed by 1 cu. ft. of 
air per minute, having a pressure of 100 lb. gage, being admitted to 
and expanded adiabatically in an air engine with 1/4 cut-off. Atmos- 
pheric pressure = 14.7 lbs. 

For 1/4 cut-off 7i=47 2 =4 cu. ft. 

and Pi = (100+ 14.7) (1/4) »-«• = 16.3 lb. per sq. in. 

Horse-power= ^[ll*^ '-^^^-U.lXi] = 0.733. 

116. Modified Power Values for Practical Air-engine Prob- 
lems. — In practical computations, the theoretical formulas, ex- 
pressing the energy residing in a quantity of compressed air 
for doing useful work, must be modified for the same reasons 
explained in Article 74. 

It is customary to subtract 15 per cent, from the theoretical 
values in order to obtain the actual work that an air engine may 
be expected to perform under normal conditions. 



CHAPTER XIII 

EFFECT OF LOSS OF HEAT, GENERATED DURING COM- 
PRESSION, ON THE ULTIMATE USEFUL ENERGY RE- 
SIDING IN A GIVEN QUANTITY OF COMPRESSED AIR 

117. By an accepted law of thermodynamics, work and heat 
are mutually convertible at the ratio of about 778 ft.-lb. of work 
for every B.T.U. 

In Article 41a it was stated that the work expended in com- 
pressing air is all converted into heat. According to the law 
quoted, we should expect the compressed, and therefore heated, 
air to be capable of performing useful work, equal to the amount 
expended in compressing it. Neglecting friction in the air 
engine, this would actually be the case, if the compressed air could 
be used immediately after compression and before it has lost 
any of its heat. 

If, on the other hand, the compressed air be allowed to cool 
down to the temperature which it possessed before compression, 
as happens in all compressed air installations, it would seem 
logical, by applying the same law quoted above, to reason as 
follows : 

Since the work of compression is all converted into heat, the 
ability for doing useful work must have disappeared after all 
this heat has been abstracted. 

In the following articles it will be shown: 

a. That the work of compression is all converted into heat. 

b. That, after all the heat of compression has been abstracted, 
there still remains in the compressed air a certain amount of 
energy for doing useful work. 

c. That this is due to the energy residing in the air before 
compression. 

a. Referring to Fig. 17, the total work of compressing adia- 
batically a volume Vi cubic feet of free air from an absolute pres- 
sure Pi to an absolute pressure P 2 is represented by the area 
MABR. Expressed in foot-pounds, it is equal to 144 times the 
numerical value of this area. 

8 113 



114 



COMPRESSED AIR 



In Article 44 we found: 



Area MABR = 



P2V2-P1V1 



therefore, total work of compression 

TFi= 144 P2F n 2 ~^ lFl foot-pounds. 



(1) 

(2) 



Let Pi = ] 4.7 lb. absolute pressure per square inch. 
P 2 = 89.7 lb. absolute pressure per square inch. 

= 75 lb. gage. 
Vi = 13.09 cu. ft. which is the volume of 1 lb. of free air at 

sea level and at 60° Fahr. 
n = 1.406. 



K- V* H, 




Fig. 17. 
From equation (7), Article 41, deduce: 

Pi\ n 



Vi \pJ 



wh 



/PA n /14 7\ °* 71 

ence 7 2 = 7 1 (y) =13.09 (^~) = 3.62 cu. ft 



Substituting values in equation (2) we get: 
,89.7X3.62-14.7X13.09 



TFi = 144 



0.406 



=47,000 ft.-lb. 






(3) 



(4) 



EFFECT OF LOSS OF HEAT 115 

After the air has been compressed adiabatically to an absolute 
pressure P 2 its absolute temperature will be according to equation 
(11), Article 41: 

n-l 

/P n \ n /8Q 7\ °" 29 

T 2 = T 7 ! \j±) = (60+461) ( j~ j = 880° absolute (5) 

= 419°Fahr. 

After compression, the original pound of air occupies a volume 
T 2 = 3.62 cu. ft. and has a temperature of 419° Fahr. which is 
(419 — 60) =359 degrees more than its initial temperature. 

Now, we can imagine a volume V 2 of air weighing 1 lb. to have 
a temperature of 60° Fahr. If we raise the temperature of this 
air by (T 2 -T x ) = (880-561) =359 degrees without changing its 
volume, we heat under constant volume. The specific heat C v 
of air in this case is 0.168 and the amount of heat put into this 
pound of air, expressed in B.T.U.'s. is 

C V (T 2 -Ti) =0.168X359 = 60.3 B.T.U.'s. 

Expressed in foot-pounds it is : 

i^(7 7 2-7 7 i) = 131.6X359 = 47,000 ft.-lb. (6) 

A comparison of equation (6) with (4) shows that the mechan- 
ical equivalent of the heat required to raise the temperature of 
] lb. of air from an absolute temperature Ti to an absolute 
temperature T 2 is identical with the mechanical energy expended 
in compressing adiabatically 1 lb. of atmospheiic air having an 
absolute temperature T\ to a pressure which raises the tempera- 
ture of the air to an absolute temperature T 2 . In other words, 
the mechanical work of compressing air adiabatically is all con- 
verted into heat energy. 

b. If we now allow this volume F 2 = 3.62 cu. ft. of compressed 
air, having a temperature of 419° Fahr., to cool down to initial 
temperature of 60° Fahr. under constant volume, its pressure 
will decrease to a pressure P 3 , which we find from the formula: 

7\ 521 

P 3= P* = 89.7 x =53.2 lb. absolute. 

I 2 00U 

The energy residing in this volume F 3 = 3.62 cu. ft. of air for 
doing useful work in expanding adiabatically down from an 
absolute pressure of 53.2 lb. to atmospheric pressure is represented 



116 



COMPRESSED AIR 



by the area BCGF in the diagram, Fig. 18, and expressed in 
foot-pounds it is 144 times the numerical value of this area. 
From article 110 we deduce: 



Hence energy 



Area BCGF 



W =144 



PzV%-PiVi 
n-1 

P3V2-P1V1 

n-1 



K-v,-— t 




Fig. 18. 

Applying it to the case in hand : 

P 3 =53.2 lb. absolute per sq. in. 

V 2 =3.62 cu. ft. 

Pi = 14.7 lb. per sq. in. 



/Pq\ n /^ 2\ °' 71 

V x = V 2 (p 3 ) =3.62 (y^j = 9.02 cu. ft. (From equa- 
tion 13, Article 41.) 
n =1.406. 

Hence W-144X 53-2X3.62-14.7X9.02 ^^ ft ^ 

Comparing this with the work of compression, we have: 
21,300 



47,000 



= 0.45 = 45 per cent. 



EFFECT OF LOSS OF HEAT 117 

That is, theoretically, after cooling down to initial temperature, 
there still remains in the compressed air energy for doing expan- 
sive work to the amount of 45 per cent, of the energy expended 
in compressing it. 

Referring to the diagram in Fig. 17, it will be noted that part 
of the total work of compression represented by the area MABR 
is performed by the atmospheric air rushing into the cylinder 
behind the piston during the compression stroke and not by 
energy furnished by the compressor. This work is represented 
by the area MAFR. 

In practice, the air, after being compressed, is delivered into 
the receiver. The work of delivery is jointly performed by the 
compressor and by the atmospheric air. The compressor's 
work is represented by the area FBCD and the work of the atmos- 
phere by the area RFDO. The net work of compression and 
delivery done by the air compressor alone is represented by the 
area ABCD. The compressor's share of delivery work is always 
available for doing useful work in the air engine because in forcing 
a volume of compressed air from the air-cylinder into the receiver, 
an equal volume of air is displaced therein, and this displacement 
process is extended into the pipe line and finally into the air 
engine, where, in making room for itself, this volume of compressed 
air drives the piston forward, and thus does useful work. 

It may be asked: What becomes of the energy contributed 
by the atmospheric air toward compression and delivery which is 
represented by the area MADO in Fig. 17? 

This energy is actually stored up in the compressed air when 
the latter leaves the compressor. It could do useful work if it 
were practicable to exhaust the air from the engines into a vacuum. 
But since we must exhaust against atmospheric pressure, the 
energy is consumed in the process of exhaustion and is therefore 
not available for useful work. It is not included in the formulas 
expressing power to be furnished by the compressor because it is 
furnished gratis by the atmosphere; and it is not included in the 
formulas expressing the useful work which a volume of compressed 
air can perform, because it is not available for such work. 

The following example shows the effect of heat loss upon the 
total power stored up in a mass of air by the compressor. 

Example. — To compress adiabatically in one stage 100 cu. ft. of free 
air per minute at sea level to 60 lb. gage and deliver it into the 
receiver, requires (theoretically) 13.40 h.p. (from column 4 Table V). 



118 



COMPRESSED AIR 



If the temperature of the free air was 60° before compression, after 
compression it will be 375° Fahr. (column 6 Table V) and the volume of 
the compressed air will be 31.44 cu. ft. (column 5 Table III) 

If used immediately after compression, before having lost any heat, 
it could do work (theoretically) to the amount of 13.40 h.p. by expanding 
adiabatically down to atmospheric pressure. 

But if allowed to cool, before use, to initial temperature under con- 
stant volume, the pressure will decrease to a pressure P 3 which we find 
from the following formula : 



P 3 =P 2 ^ = (60+14.7) 



60+461 



= 46.6 lb. absolute. 



! T 2 v ' ' 375+461 

A volume of 31.44 cu. ft. of air per minute at 46.61b. absolute, if allowed 

to expand adiabatically down to atmospheric pressure could perform 

(theoretically) an amount of work found from equation (1) Article 111 : 



Horse-power : 



33 



44 n P 2 V 2 L /^f\V] 
,000(72-1) L \PJ J 



= 144X1.406X46.6X31 
33,000X0.406 

which is about 47 per cent, of the power expended in compression and 
delivery. 

When friction and other imperfections are taken into account, this 
percentage decreases materially. 

Adding 15 per cent, to the power of production we get 15.43 h.p. 

Subtracting 15 per cent, from the available theoretical energy we get 
5.35 h.p. and the comparative value shrinks to 35 per cent. This is 
further diminished by losses during transmission which are pointed out 
under Articles 93-94 and 97-105. 

c. The answer to the question, why energy still remains in the 
compressed air after all the heat of compression has been dis- 
sipated, is that a certain capacity for work resides in the air 
which is due to the latter's ability to expand when the proper 
conditions prevail. 

Such conditions could be brought about by confining a volume 
of atmospheric air in a cylinder under a piston and then create a 
partial vacuum on the other side of the piston; the atmospheric 
air in the cylinder would expand and push out the piston, that is, 
perform work. But creating a vacuum requires extra work, and 
is therefore not of practical application in air engines. 

As a matter of fact, after all the heat generated during compres- 
sion of a volume of air has been dissipated, the compressed air 
possesses no more energy than it did before compression, but 



VALUE OF "n" 119 

part of the energy which it did possess has, by mechanical 
compression, been made available for doing useful work. 

To do work, however, the air requires energy in the form of 
heat and while expanding, it consumes heat that was contained in 
its mass before compression. As a consequence the temperature 
of the expanded air falls below that of the surrounding atmos- 
phere. The amount of heat consumed is equivalent to the 
amount of work performed and equal to the amount of heat that 
would be generated in compressing this air from the pressure at 
which it exhausts from the air engine to the pressure at which it 
enters the same. 

The consumption of heat from the mass of the expanding air 
is manifested by the cold created in and around the cylinders of 
an engine using air expansively. Theoretically this is exactly 
the reverse of the generation of heat in the air cylinders of a 
compressor. 

117a. Determination of the Value of "n," used in adiabatic 
compression and expansion formulas: 

From equation (6), Article 117, we have: 
Work of adiabatic compression of 1 lb. of free air: 

W = K V (T 2 -Ti) foot-pounds (1) 

in which K v = specific heat of air at constant volume, expressed 

in foot-pounds. 
T 2 = final absolute temperature of air after being 

compressed to an absolute pressure P 2 . 
T\ = initial absolute temperature of air at an absolute 

pressure Pi. 

In the diagram, Fig. 17, the area MABR represents the mechan- 
ical work of compressing a volume V\ of air from an absolute 
pressure Pi to an absolute pressure P 2 , the volume of compressed 
air being V 2 . 

From equation (1) Article 117: 

* -mr A r*-r* P2 *2 Pi' 1 ,^s 

Area MABR = * — (2) 

n— 1 v ' 

Let Pi and P 2 be the absolute pressures in pounds per square 
foot; then the work performed, corresponding to area MABR: 

W = 2 _ j -— ^foot-pounds (3) 



120 COMPRESSED AIR 

Let, furthermore, V\ and V 2 represent volumes occupied by 1 lb. 
of air when under an absolute pressure of Pi or P 2 respectively; 
then from equation (5) Article 20: 

PiVt = RT X 
and P 2 V 2 = RT 2 

Substituting these values in equation (3) we have: 

RT2 — RT1 R(T 2 —Ti) 

W = z — = = — (4) 

n— 1 w—1 v J 

From equation (7) Article 20 we have: 

R = Kp — K v 

Substituting in equation (4) we get: 

71—1 V ; 

This work is equal to the work expressed by equation (1), there- 
fore: 



K V (T 2 -T l ) = 



(K P -K V )(T S -T{) 



n-1 
or nK v — K v = K p — K v 

whence ^ = ^r (6) 

K v 

as first stated under Article 40. 












CHAPTER XIV 
INTERNAL OR INTRINSIC ENERGY OF AIR 

118. A capacity for doing useful work by expanding against an 
external resistance, resides in a mass of air as long as its tempera- 
ture is above the absolute zero. A pound of atmospheric air 
at 60° Fahr. at sea level, for instance, may be conceived as the 
outcome of a pound of air at the temperature of absolute zero 
to which a sufficient amount of heat has been supplied to raise 
its temperature by (461+60) =521° Fahr., and its pressure to 
14.7 lb. above the vacuum. 

According to a law of thermodynamics, quoted in previous 
articles, the heat energy in this pound of air, corresponding to a 
temperature of 521° above the absolute zero, may be converted 
into mechanical energy whenever the conditions permit it. The 
capacity of air of performing work, due to its temperature above 
the absolute zero, is called the internal or intrinsic energy of air. 
It is independent of pressure, that is, a pound of atmospheric 
air at a temperature of 60° Fahr., has the same intrinsic energy 
as a pound of air under a pressure of 100 lb. having the same 
temperature of 60° Fahr. (See Articles 119 and 120.) 

When applied to practice, there is a vast difference, however, 
between the pound of atmospheric air and the pound of air at 
100 lb. pressure. In the first case none of the intrinsic energy 
residing in the air is available for useful work under ordinary 
conditions, whereas in the second case a portion of the intrinsic 
energy has by mechanical compression been made available for 
such work. 

This may be better understood by comparison with the more 
familiar generation of water-power. Water flowing down a 
river possesses intrinsic energy, that is, a capacity for doing 
useful work when the proper conditions exist. These conditions 
are brought about by building a dam across the river which 
raises the water level and thus produces a head, the height of 
which, together with the amount of water delivered, determines 
the amount of useful work the water is capable of performing. 
By building the dam we have added nothing to the intrinsic 

121 



122 COMPRESSED AIR 

energy of the water, we have only made available a portion of 
that energy for performing useful work. 

In an analogous manner, by compressing air isothermally, 
we add nothing to its intrinsic energy, we merely make a portion 
of that energy available for doing useful work. In actual prac- 
tice, compression is more or less adiabatic, imparting heat energy 
to the air, which, however, is subsequently lost in transmission. 
The condition of the air before use is therefore the same as after 
isothermal compression. 

The conception of internal or intrinsic energy indicates that 
when air expands without doing work, it loses none of its heat, 
because the intrinsic energy remains unchanged. The truth 
of this fact was first proved experimentally by Joule and the fact 
itself is known as Joule's Law. 

119. Intrinsic Energy of a Pound of Atmospheric Air at a 
Temperature of 60° Fahr. — The specific heat of air under constant 
pressure is 0.2375, therefore the quantity of heat, that is, the 
number of B.T.U.'s required to raise the temperature of 1 lb. of 
atmospheric air from absolute zero to 60° Fahr. is: 

(461 +60) X0.2375 = 123.74 B.T.U.'s 

and the amount of work corresponding to this quantity of heat is 
123.74X778 = 96,268 ft.-lb. This is the intrinsic energy of 1 lb. 
of atmospheric air at 60° Fahr., none of which, however, is avail- 
able for useful work under ordinary circumstances. 

120. Intrinsic Energy of a Pound of Air at 100 lb. Gage and 
at 60° Fahr. — If permitted to expand adiabatically down to 
atmospheric pressure against an external resistance, this pound 
of air would perform work and therefore consume an amount of 
heat equal to the amount that was generated during adiabatic 
compression. The theoretical temperature of the air after expan- 
sion is deduced from formula (11) Article 41: 

n-l 

T, = r(5)" =(60+461) (55$-) ~ 

= 286.55 degrees absolute. 
= -174.45° Fahr. 

The drop in temperature is therefore (60+174.45) =234.45 
degrees and the number of B.T.U.'s consumed during expansion 
would be 234.45X0.2375 = 55.68 B.T.U.'s. 



INTERNAL OR INTRINSIC ENERGY OF AIR 123 

The equivalent of 55.68 B.T.U.'s expressed in foot-pounds is 
55.68X778 = 43,321 ft.-lb. This is the amount of intrinsic 
energy residing in the pound of compressed air which is available 
for doing useful work. 

But there still remains energy in the air which might be used 
if it were possible for the air to expand down to the absolute 
zero of pressure, in which case the temperature of the air would 
drop from 286.55 absolute to the absolute zero of temperature. 
This represents a consumption of heat units equivalent to 
(286.55X0.2375) =68.065 B.T.U.'s and these 68.056 B.T.U.'s 
present work equivalent to (68.056X778) =52,947 ft.-lb. This 
latter energy is not available for useful work under ordinary 
circumstances. 

The total intrinsic energy of the pound of air at 100 lb. gage 
and 60° Fahr. is (43,321+52,947) =96,268 ft.-lb. which is the 
same as the total intrinsic energy of the pound of atmospheric air 
at 60° Fahr. 



CHAPTER XV 
THE EFFICIENCY OF A COMPRESSED-AIR SYSTEM 

121. This is evidently the ratio between the ultimate work 
performed by the engine using compressed air and the power 
required to compress that air in the compressor. 

In computing this efficiency all the possible losses must be 
taken into consideration which may occur from the moment a 
certain quantity of air enters the compressor until it is exhausted 
from the air engine. 

These losses are chargeable: 

1. To air being taken into the compressor from the engine 
room rather than from a cooler place. This results in a lesser 
quantity (weight) of air being taken into the cylinder per stroke, 
thereby increasing the power required to compress a given 
quantity of air per unit of time. This loss can be prevented by 
making adequate provisions for the air in-take from the coolest 
outside place around the compressor building (see Article 87). 

2. To friction in the compressor. This will amount ordinarily 
to a power loss of from 15 to 20 per cent. It can be reduced by 
good workmanship to about 10 per cent, but cannot be avoided 
altogether. 

3. To a series of imperfections in the compressing cylinders, 
such as insufficient supply of free air, difficult discharge, defective 
cooling arrangments, poor lubrication, etc. 

4. To heat generated during compression which increases the 
power required for compressing a given quantity of air, for which 
there is no return, as the heat is afterward dissipated in trans- 
mission. 

5. To loss of pressure in the pipe line, due to friction, etc. 

6. To friction and fall of temperature during expansion of the 
air in the cylinder of the air engine. 

7. To leaks in the compressor, the pipe line, and in the air 
engine. 

Example. — Let us follow a volume of 10 cu. ft. of free air, having an 
initial temperature of 60° Fahr., from the moment it is taken into the 
cylinder of the compressor until it is exhausted from the air engine. 

124 



EFFICIENCY OF A COMPRESSED-AIR SYSTEM 125 

Kef erring to the example under Article 87, we found that it took 55,600 
ft.-lb. of work to compress these 10 cu. ft. of free air in one stage to 70 
lb. gage, and that we finally deliver into the pipe line a volume of 2.68 
cu. ft. of air having an absolute pressure of 50 lb. and a temperature of 
60° Fahr. 

Assuming that the pipe line is so dimensioned that the loss of pres- 
sure is 5 lb., then the compressed air which is delivered at the end of 
the pipe line has an absolute pressure of 45 lb. and its volume has ex- 
panded at constant temperature to 

7 2 =Fip= 2.68^ = 2.98 cu. ft. 

According to equation (1) in Article 113, a volume of 2.98 cu. ft. of air 
at 45 lb. absolute if admitted to and allowed to expand adiabatically 
down to say, 16.5 lb. absolute in an air engine, is capable of doing use- 
ful work (theoretically) to the amount of: 

W n = 144 [p 2 7 2 +^^™i^- PoFl ] foot-pounds 

in which P 2 = 45 lb. per square inch 
V 2 = 2.98 cu. ft. 
Pi = 16.5 lb. per square inch 

V x = V 2 ^ 2 \ n =6.08cu. ft. 

P a = 14.7 lb. per square inch 
n = 1.406 

[■ 

= 18,400 ft.-lbs. 



„ ,, , | ! -x2.98+ 45X ^ 8 - 4 1 6 6 5X6 ^- -14.7X6.08 



Deducting 15 per cent, for friction, etc., gives: 

Work performed by air engine, 15,600 ft.-lb. 
Work of compression and delivery, 56,600 ft.-lb. 

Efficiency of whole system = ft ' = 28 per cent. 

Practical tests frequently show lower efficiencies than those obtained 
by calculation, due to leaks in compressor, pipe line, air engine, and to 
other imperfections. If air is used in the motor at full pressure during 
the entire stroke as, for instance, in air drills (see Article 109), the 
efficiency sinks to its lowest level. 

As has been pointed out, the use of compound compressors with 
adequate cooling devices and the use of higher initial pressures will 
result in higher mechanical efficiency of the whole system. One of the 
means employed at present to increase this efficiency is a system known 
as "Reheating" which is described under Article 122. 



CHAPTER XVI 
REHEATING OF COMPRESSED AIR 

122. In preceding articles it has been shown that the available 
energy residing in a given weight of compressed air at the end 
of the pipe line is considerably less than that which the same 
weight of compressed air could develop immediately after leaving 
the compressor. This is due to the fact that the volume of a 
given weight of air, having a given pressure, is smaller at the 
lower temperature which prevails at the end of the pipe line than 
that which it occupies when leaving the compressor at a high 
temperature, and to the fact that the available power residing in 
compressed air is dependent on volume as well as on pressure. 

This has led to the introduction of a process known as " Reheat- 
ing." By this process the volume of the compressed air at the 
terminal may be, by heating, increased so as to partly or com- 
pletely make up for loss of power in transmission. 

To accomplish this result there must be an expenditure of fuel. 
This expense, however, is very light. For the average air engine 
it amounts to about one-seventh of the fuel that would be 
originally required to compress air so that it would be in a condi- 
tion to develop an equal power, it being assumed that coal is the 
fuel used. This is due to the fact that the average efficiency of a 
Corliss steam engine does not exceed 10 per cent., based on the 
total heat value of the fuel, whereas in reheating in a proper 
heater 70 per cent, of the heat value of the fuel may be utilized. 
The increase in efficiency resulting from reheating makes it 
possible to use a much smaller air compressor for performing a 
given amount of work. 

In addition to increasing the efficiency, the reheating of com- 
pressed air also prevents the freezing of the exhaust ports of air 
engines which often becomes troublesome when air containing 
considerable moisture is exhausted at temperatures below the 
freezing point. 

Let us assume that at the end of the pipe line we have 1 cu. ft. 
of air at 75 lb. gage, and at a temperature of 60° Fahr. and that 
we wish to double this volume by reheating. 

126 



REHEATING OF COMPRESSED AIR 127 

The volume of free air which must be compressed to make, 
after being cooled down to 60° Fahr., 1 cu. ft. of air at 75 lb. gage, 
we find from the equation 

89.7 
whence V = 1 X ~tt i 7 = 6.10 cu. ft. 

To compress adiabatically in one stage 6.10 cu. ft. of air to 75 lb. 
gage and deliver it into the receiver or the pipe line requires 
work to the amount of 

= —. j— ( -p ) — 1 foot-pounds (theoretical) 



144X1.406X14.7X6.10 r/89.7 



0.29 



0.406 [( W ) -l] =30,832 ft,lb. 

Adding 15 per cent, for friction we have 
W n = 35,457 ft.-lb. 

If the compression is to be accomplished by a steam engine cut- 
ting off at 1/4 stroke the number of cubic feet of 75 lb. steam re- 
quired to do the work is found as follows : 

TF n = 144P w y 1 

in which, W n = work in foot-pounds = 35,457 

P m = mean effective steam pressure in pounds per 

square inch = 37.8 
Vi = volume of steam in cubic feet after expansion 
= four times the volume we wish to ascertain. 

Introducing values 35,457 = 144 X37.8Fi 

35 457 
Whence Fl= 144X37.8 = 6 " 52 

Dividing by 4 ^- = 1.63 

1 fi*^ 
Adding 15 per cent. 1.63+^- X 15 = 1.87 cu. ft. of 75 lb. 

steam, or practically 2 cu. ft. 
In other words, to compress a certain mass of air by steam pres- 
sure so as to furnish 1 cu. ft. of compressed air at 75 lb. gage and 



128 COMPRESSED AIR 

at 60° Fahr., requires practically 2 cu. ft. of steam at 75 lb. Now, 

1 cu. ft. of steam at 75 lb. weighs -j^~ = 0.206 lb. (Kinealy steam 

engine). Total heat required to make 1 lb. of steam at 75 lb. 
from water having a temperature of 60° Fahr., is: 

1179- (60-32) = 1151 B.T.U.'s (Kinealy). 

Total heat required to make 2 cu. ft. of 75 lb. steam, is: 

2X1151X0.206 = 474 B.T.U.'s 

From this it follows that the number of heat units required to 
produce by steam energy 1 cu. ft. of air at 75 lb. gage and at 60° 
Fahr. is 474 B.T.U.'s. 

The temperature of 1 cu. ft. of air at the end of the pipe line is 
(60+461) =521 degrees absolute. To double the volume at 
constant pressure, we must double the temperature, that is, the 
absolute temperature of the 2 cu. ft. of air at 75 lb. gage would 
be 1042 degrees and the increase in temperature is 

1042-521=521 degrees. 

The weight of 1 cu. ft. of air at 75 lb. gage and at 60° Fahr. is 
from Article 24: 

^2 = 2.7077^ 
i i 

7fj_l 147 
^ = 2.7077-^^=0.466 lb. 

The specific heat of air at constant pressure is 0.2375. There- 
fore, to raise the temperature of 0.466 lb. of air at constant pres- 
sure by 521 degrees requires 

0.466X0.2375X521=58 B.T.U.'s 

This shows that to produce an extra cubic foot of air at 75 lb. 
by a steam-driven compressor would require 474 heat units, 
whereas by reheating we have at an expenditure of only 58 heat 
units made 2 cu. ft. out of the original 1 cu. ft. of compressed air. 

The additional power cost of reheating, expressed in heat units, 
in this case is therefore only one-eighth of that of compression by 
steam energy. 

In practice, no attempt is made to double the volume of com- 
pressed air, after it arrives at the air engine, because at tempera- 



REHEATING OF COMPRESSED AIR 



129 



tures much above 300° Fahr. the lubricant in the motor is apt to 
charr, causing severe cutting action on the valves, rods, and 
stuffing boxes. 

To increase the volume of the compressed air by reheating 
from 40 to 50 per cent, is considered quite satisfactory. Beyond 
that, the air is heated only sufficiently to compensate for heat loss 
during its passage from the heater to the air engine. To minimize 
this loss, the heater should be placed as near the point of use as 
circumstances will permit, and the pipe between the heater and 
the machine should be well covered. 




Fig. 19. — Sullivan Air Reheater. 

In the following articles are illustrated and described two types 
of reheaters which are being used in operations where compressed 
air is employed for power purposes. 



AIR REHEATERS 

123. The Sullivan air reheater, illustrated in Fig. 19, consists 
of a series of hollow annular rings, forming the heating surface, 



130 



COMPRESSED AIR 







REHEATING OF COMPRESSED AIR 131 

surrounded by asbestos matting and enclosed in a sheet-steel 
shell. The rings and shell rest upon two cast-iron rings, lined 
with fire brick, forming the fire box. The latter is provided with 
dumping grate and doors as shown. The hot gases after cir- 
culating around the rings, escape through the hood and smoke 
pipe on top. 

Air enters the reheater at the top and is forced to take a cir- 
cuitous passage through the annular rings by means of baffle 
plates so that it comes in contact with the heating surface. The 
heated sections are designed so as to prevent leakage in the 
joints, due to expansion. The heated air leaves the reheater by 
a flanged opening in the bottom ring, similar to that by which it 
enters the top ring. 

These reheaters are designed for burning coal, but may be 
adapted for oil fuel. 

124. The Sergeant air reheater, made by the Ingersoll-Rand 
company, is shown in Fig. 20. The air enters at the top of the 
heater, is forced in thin sheets through the annular space between 
the inner shell (A) and outer shell (B) of the heater, and leaves 
the latter at the bottom. The increased air space between in- 
take and discharge pipes, due to the conical shape of the castings, 
provides for the expansion of the air in heating. The outer shell 
is surrounded by a mantel (C) of sheet iron and the space 
between the latter and the shell (B) is packed with asbestos. 

125. Other reheaters, using steam, are successfully employed 
for surface work. Those described are, in general, not suitable 
for underground work in mining operations where the smoke 
from coal or oil fuel is objectionable. Although a number of 
appliances have been tried for such work, no heater that could be 
used satisfactorily under all conditions has made its appearance 
as yet. 



PART IV 

AIR COMPRESSORS AND ACCESSORIES 

CHAPTER XVII 

EXAMPLES OF MODERN AIR-COMPRESSORS OF THE 
RECIPROCATING TYPE 

126. In the following articles a few prominent types of com- 
pressors, selected at random, are illustrated and described for the 
purpose of demonstrating the practical application of the theo- 
retical principles discussed in preceding chapters. 

The design and construction of compressors is a subject of 
mechanical engineering. No attempt has been made here to 
treat this subject in detail. But the writer believes that a few 
general remarks on the construction of modern compressors will 
prove helpful to the engineer in making a judicious selection of 
machines, when called upon to install a compressed-air plant. 

127. Fig. 21 gives plan and elevation of five types of steam- 
driven compressors, showing some, but by no means all the 
possible combinations of steam and air cylinders. Compressor 
builders, as a rule, designate them either as " straight-line" or 
" duplex" compressors. 

OPERATION OF STEAM-DRIVEN, STRAIGHT -LINE COMPRESSORS 

128. If we study the section of the steam and air cylinders of 
a compressor as shown in Fig. 22 and assume the piston to move 
in the direction of the arrow, we note the following conditions : 

In the air cylinder, at the beginning of the stroke the resistance 
to the advance of the piston is practically zero. The pressure, 
however, begins to rise at once, steadily increasing the corre- 
sponding resistance against the piston until close to the end of 
the stroke at A the receiver pressure is reached, when the dis- 
charge valves open. From this point to the end of the cylinder 
at B the piston travels against a practically uniform maximum 
pressure in delivering the air into the receiver. 

On the return stroke, the compressor being double-acting, the 
resistance is again zero at the beginning of the stroke and maxi- 
mum for the latter part of it. 

132 



AIR-COMPRESSORS OF THE RECIPROCATING TYPE 133 

In the steam cylinder the development of power is precisely the 
reverse of the distribution of resistance in the air cylinder. 

Here the pressure is maximum at the beginning of the stroke 
and practically uniform until cut-off occurs at D. Then the 



© 



SIMPLE STEAM SIMPLE AIR 



STRAIGHT LINE (2) 

SIMPLE STEAM COMPOUND AIR 




-o 



' 


STEAM 




AIR 




4 — > 


1 





FLY WHEEL 


\ rl H'.nt 


1 


s — -H A1 i n -[^ IH | 



INTERCOOLEF 



.Y WHEEL FLYWHEEL 

® DUPLEX @ 

SIMPLE STEAM SIMPLE AIR SIMPLE STEAM COMPOUND AIR 





A 



CRANK DISK 



CRANK DISK 



2 FLY WHEEL 



steam -E£] 



NTERCOOLER 



COMPOUND STEAM 



COMPOUND AIR 




i 



CRANK DISK 



] FLY WHEEL 




DIAGRAM 

SHOWING 

OUTLINE ELEVATION AND PLAN 

OF FAMILIAR TYPES 

OF STEAM-DRIVEN 

AIR COMPRESSORS 



Fig. 21. 



pressure rapidly falls all the way to the end; so that in any 
compressor of the straight-line type the steam power is in excess 
of the work to be done at the beginning of the stroke in either 
direction and inadequate to overcome the resistance of the air at 
the other end of the stroke, except with the assistance of fly- 
wheels. 



134 



COMPRESSED AIR 



C D 



A B 





AIR OUTLET 




Fig. 23. — Sullivan Straight-line Steam-driven Single-stage Compressor. 



AIR-COMPRESSORS OF THE RECIPROCATING TYPE 135 

The excess pressure at the beginning of the stroke causes the 
fly-wheels to acquire momentum which they give off at the 
end of the stroke to overcome the excess of the air-piston 
resistance. 

This unequal application of power to resistance prevents 
smooth running in this class of compressors and causes severe 
strains in the moving parts. 

129. Type (1). Straight-line, Steam-driven, Single-stage 
Compressor. — Fig. 23 illustrates a compressor of this type, built 
by the Sullivan Machinery Company. These machines have one 
steam and one air cylinder, set tandem on a common piston rod, 
and two fly-wheels, usually driven by outside connecting rods 
from a cross-head, which slides between guide plates connecting 
the steam and air cylinders. They are built and used for pres- 
sures up to 90 lb. 

Advantages. — Compressors of this type are self-contained, sim- 
ple in construction, strong and compact, and of moderate price. 
Compared with duplex machines of equal capacity they occupy a 
smaller floor space and do not require as expensive foundations 
as the latter. 

Disadvantages. — When running below a certain speed, most 
straight-line compressors have a tendency to stick on centers. 
Hence an early cut-off in the steam cylinder is not possible. 
Such compressors usually run with 5/8 to 3/4 cut-off, resulting 
in high-steam consumption, averaging from 40 to 50 lb. per horse- 
power hour. 

130. Type (2). Straight-line, Steam-driven, Two-stage Com- 
pressor. — Fig. 24 illustrates a machine of this type, built by the 
Sullivan Machinery Company. These machines have one steam 
and two air cylinders, set tandem on a common piston rod. 
The air is compressed in the larger (low-pressure) cylinder to an 
intermediate pressure, whence it passes by way of an inter-cooler 
into the smaller (high-pressure) cylinder, where it is compressed 
to the final pressure. 

Advantages. — If properly designed and cared for, these machines 
have the advantages pertaining to compound compression as 
pointed out under Article 75. 

Disadvantages. — In addition to the disadvantages pointed out 
for Type (1), which apply to all straight-line compressors, the 
compounding of the air cylinders complicates the machine, 
increases the relative cost of it for the work it does, makes all 



136 



COMPRESSED AIR 




o 
U 

o 

fafl 
o3 



CO 

.5 

bJD 



AIR-COMPRESSORS OF THE RECIPROCATING TYPE 137 







i 

o 
O 



138 



COMPRESSED AIR 



parts less accessible for adjustment, while it has left the machine 
with its usual inability to run at slow speed. 

131. Operation of Steam-driven, Duplex Compressors. — A 
duplex air compressor is, in essential effect, a combination of 
two straight-line machines, so far as the steam and the air cylin- 
ders are concerned, with a single crank shaft and a single fly- 
wheel serving both, there being a single connecting rod for each 
side and a single crank on each end of the shaft. 

In the duplex compressor the operating conditions are in 
decided contrast to those described for the straight-line com- 
pressors. 

Quartering Cranks. — The first special feature of advantage of 
the duplex machine is in the arrangement of the cranks in relation 
to each other upon the ends of the shaft. These are set with 
one of the cranks a quarter of a circle in advance of the other, 
the result of which is to so time the movements of the pistons on 
the two sides of the machine that one will be at nearly midstroke 
when the other is at the beginning or end of its stroke. The two 
sides thus alternately help each other over the hard places, and, 
while not under nearly as great obligation to the fly-wheel, their 




Fig. 25. 



action is much steadier and so free from excesses of pressure over 
resistance or of resistance over pressure, that the rotation is more 
uniform. The practical limit of speed is lowered to perhaps 
one-quarter of the lowest speed permissible in the straight-line 
type, so that, if the cut-off on the steam cylinder is properly set, 
the machine may be made to automatically stop and start itself 
and to run at any speed down to the lowest, as the air consump- 
tion may require. Waste of power and steam, consequent upon 
the necessity of running at high speed to prevent centering, 



AIR-COMPRESSORS OF THE RECIPROCATING TYPE 139 

will be avoided. The conditions of pressure and resistance are 
illustrated graphically in the diagram Fig. 25. 

The two steam and air cylinders of the compressor are shown 
in the diagram one above the other. In the two upper cylinders 
minimum power in the steam cylinder is being applied to maxi- 
mum resistance in the air cylinder at the end of the stroke. In 
the two lower cylinders excess power is being applied to small 
resistance at midstroke, the surplus pressure acting to carry the 
compressor past the center of the upper cylinders. 

Similar conditions can be shown for other positions of the 
pistons. 

131a. Compared with straight-line machines, duplex compres- 
sors offer several disadvantages which should be taken into con- 
sideration when planning an installation. 



I 


™^W»?i 




lift 


BP ■•-•■)■ j 

n % 4 

j. > U — — «~~ .-' 


SL J 


i 





Fig. 26. — Laidlaw-Dunn-Gordon Duplex, ^team-driven, Single-stage 

Compressor. 

For any given output of air they are more expensive in first cost 
and up-keep, for there is double the machinery. There are double 
the chances of delays, for either side may be necessarily stopped 
and then all the air is shut off until adjustments can be made to 
both machines. A heated journal on either side will stop both. 
The friction of the duplex machines exceeds on an average by 
about 5 per cent, the friction of two machines working separately. 

All duplex compressors occupy much more floor space than 
straight-line machines of the same capacity, consequently require 
larger and more costly buildings and foundations. 

132. Type (3). Duplex, Steam-driven, Single-stage Com- 
pressor. — Fig. 26 shows a machine of this type, built by the 



140 



COMPRESSED AIR 





Fig. 27. — Ingersoll-Rand Duplex Steam-driven Two-stage Compressor. 






AIR-COMPRESSORS OF THE RECIPROCATING TYPE 141 

Laidlaw-Dunn-Gordon Co. It is merely a combination of two 
straight-line, single-stage compressors of type (1), set on the same 
shaft with one fly-wheel instead of two. 

It combines all the advantages and disadvantages of a duplex 
compressor, pointed out in Articles 131 and 131a. Compared 
with types 4 and 5, it has the advantage that, if necessary, one 
side can be operated as a complete machine. 

133. Type (4). Duplex, Steam-driven, Two-stage Compres- 
sor. — Fig. 27 illustrates a compressor of this type built by the 
Ingersoll-Rand Co. It has simple steam cylinders and cross- 
compound air cylinders. The inlet valves of both the low- and 
high-pressure air cylinders are of the Corliss type. The inter- 
cooler is placed in the cast-iron frame, which makes the com- 
pressor more compact. 

Compressors of this type partake of all the advantages and dis- 
advantages of the duplex feature as well as of stage-compression, 
as pointed out in Article 75. One objection to cross-compound 
air cylinders in duplex machines is that under no circumstances 
can one side be operated as a complete machine. 

134. Type (5). Duplex, Steam-driven, Two-stage Com- 
pressor. — Fig. 28 illustrates a compressor of this type, built by 
the Allis-Chalmers Company, with the inter-cooler removed. 
Both air and steam cylinders are cross-compound. Inlet valves 
are of the Corliss type. It is not possible to operate one side 
of this compressor as a complete machine, on account of the cross- 
compound feature, which requires the operation of both sides 
at the same time. 

135. Other Types of Steam-driven Compressors. — For illus- 
tration of other types and combinations of steam-driven, single- 
and multi-stage compressors, the reader is referred to the cata- 
logues and bulletins of manufacturers which, besides copious 
illustrations, usually contain a large amount of useful data on air 
compression. The remarks contained in the preceding articles 
should enable the reader to draw fairly correct conclusions as to 
the merits of the one or the other type and make of compressor 
when referred to the needs of any contemplated installation. 

POWER-DRIVEN AIR COMPRESSORS 

136. A large class of compressors used in the various industries, 
are of the power-driven types. That is, they consist of one or 
more air cylinders, the piston rod of which is connected through 



142 



COMPRESSED AIR 




a 

o 
O 



X 

Q 

CO 
S-i 

o 

a 

1 
o 

1 

1 



AIR-COMPRESSORS OF THE RECIPROCATING TYPE 143 




a 

a 

o 
O 

I 

> 



144 



COMPRESSED AIR 



a connecting rod and crank to a revolving shaft, the latter being 
driven from a central power plant, or by a water-wheel, or by an 
electric motor. 

In selecting a power-driven compressor, it must be borne in 
mind that it cannot be hurried, neither can it be run at a speed 
little less than the maximum. Steam-driven machines can be 
run at variable speed to suit the requirements, but the power- 
driven compressor must always run at full speed, and variations 
of demand can only be met by unloading, either wholly or in part 
as circumstances may require. 

For unloading devices see Articles 156-160. 

Compressors of small power can be driven by belts, chains or 
gears. Moderately large powers, unless driven direct, are depend- 
ent upon ropes or belts, while for compressors of very large 
capacity direct drive seems the most satisfactory. 

BELTED, COMPARED WITH DIRECT STEAM POWER 
COMPRESSORS 

137. The question is frequently asked : Under what conditions 
is a belted compressor more advisable than one having its own 
independent steam engine? In an establishment having a large 
high-class main engine of abundant power, the belt pattern offers 
the advantage of compressing the air with the same steam econ- 




Fig. 30. — Norwalk Two-stage Compressor with Water-wheel Drive. 

omy as is obtained in the large steam engine, and will therefore 
prove more economical in first cost as well as in operation. 
Economy, however, must always be studied not in the engine 
alone, but in the compressor as well and when the air demands 
are of considerable relative consequence, the power required may 
necessitate the individual engine for the compressor. 






AIR-COMPRESSORS OF THE RECIPROCATING TYPE 145 

138. Fig. 29 illustrates a two-stage compressor of the belt 
pattern, built by the Norwalk Iron Company. The large band 
wheel serves for a driving pulley as well as for a fly-wheel and can 
be belted to the pulley on a large main drive shaft or to the pulley 
of an electric motor. 

139. Compressors with Direct Water-wheel Drive. — Fig. 30 
illustrates a compressor of this type built by the Norwalk Iron 
Company. For the band wheel a heavy fly-wheel is substituted 
and on this the water-wheel buckets are mounted. 

Where abundant water power is available for continuous 
service such compressors may be used to great advantage. 

ELECTRICALLY OPERATED COMPRESSORS 

140. Like all power-driven compressors, electrically operated 
compressors must be run at constant speed and must therefore 




Fig. 31. — Ingersoll-Sergeant Rope-driven Compressor. 

be provided with unloading devices to regulate the output, whe 
used for intermittent demand. 

10 



146 



COMPRESSED AIR 




Fig. 32. — Nordberg Electrically-driven Geared Two-stage Compressor of 

the Duplex Type. 




Fig. 33. — Ingersoll-Rand Direct-connected Electrically-driven Two-stage 

Compressor. 



AIR-COMPRESSORS OF THE RECIPROCATING TYPE 147 

Besides belt or rope driven, in which the pulley of the motor is 
connected by belt or ropes with the band wheel of the compressor, 
as shown in Fig. 31, electric motors are also geared or direct con- 
nected to the revolving shaft of the compressor. 

141. Fig. 32 illustrates an electrically driven, geared, two- 
stage compressor of the duplex type, built by the Nordberg 
Mfg. Co. The inlet valves which are of the Corliss type are 
released by an unloading device from the operating mechanism, 
when they are wide open and are kept in that position until more 
air is required. The releasing is effected by cams, operated by a 
frictionless plunger on which the air pressure acts in opposition 
to a weight. These cams throw out a latch so placed on the valve 
operating lever, that it closes the valve, while the opening is 
effected by a projection acting on the valve operating lever. 
The cams are so adjusted that first one and then the other 
engages the releasing latch. 

142. Fig. 33 illustrates a direct-connected, electrically driven, 
two-stage compressor, built by the Ingersoll-Rand Company. 



(ii \rn i: win 

IMPORTANT MECHANICAL FEATURES OF AIR COMPRESSORS 

143. Without L'"i!i^ into detail of construction, attention will 
tiled t<- the mechanical I irhich influence the 

• thai un 

.'.t- can in nm-t <a-»- !••• i \ cither del 

nr I D part- \ 

tlnir function will enable 1 1 
probable my fail . pressor 

to do its duty, and t<> apply tin- 1. such fail 

inherent un] 

INLET VAL\ 

144. The inlet valv. ompreaeor are either of th< 

n»^ held totl by sprii tnically 

mbling in th< J form and • am 

:n<\ 

145. Poppet Inlet Valves. \11 popp 

inlet «»r diacharu n-Ut essentially of three main part-: 

alve pro] tide and a sprinj • ion 

In general, poppet inlet vah 

must insure prompt : all *\*< 

osiderablc strength. Tl rottling 

inlet and hence loss of volum 

iwer to make uj> for tin- Io-n. 

passes i 
thin -tn and 

U of these 
ditiom have been pointed ou1 under \ ^r 

of tl 

146. Inlet Valves ofl Um Coii I 

I the [ngersoU-rl 9ee ] 

Us 



I BANICAL I 140 

.1 with a ■ 

mi it- inn i • h with . 

end of \al\- 

: being ma<l< 

i- maintained b - of til>«T wai 

valve stem collar, al~<> bom 

thimble "/•"' in back bona G. Lubrication for tin 
• •//•• and •'/." 

Valves of tin- < *« » r 1 i — typ< ■-iti\a-ly iin.v. .1 h 

the compree 
illustrated in I ig. 28. 




«• port i and their p 

ineui 'M»|il\ that keepi pace irith tl tin* 

machine. 
147. tagersoll-Rogief Valve. The valve illustrated u 

i In- « 1 1 — « - t \ |h . i • |ve seat 

ii.n poi te, s in- li nippi 
cushion plate H 

beld togetl 
M of ■. ah ■ / • bat hold tfa 

lui. K in oi m.i alwaj i i same pi 

.-lin.h pUte // i" Id ■ 
ral \ ah < 
\ oon si the 
agar I .'loees agm 

o the I tnd l«.w hit. ill. 

to little m 

aroposMi'li' than would be wii«- with 



150 



COMPRESSED AIR 



The absence of gears for operating the valve eliminates friction 
and since there are no rubbing parts, the valve needs no lubrication. 




Fig. 35. — Section Showing Inlet Valve in the Air Cylinder of a Modern 
Ingerso 11-Rand Compressor . 



DISCHARGE VALVES 

148. Discharge valves, like inlet valves, are either of the 
poppet or disc type or they are mechanically moved and of 
similar construction as the inlet valve shown in Fig. 34. 

149. Poppet Valves. — Fig. 36 illustrates a simple construction 
of a poppet discharge valve, used in some Ingersoll-Rand com- 
pressors. (See Fig. 10.) 

The valve proper is ground to an accurate seat, while the cap 
or valve-guide is ground to a w r ide guide surface insuring the re- 



MECHANICAL FEATURES OF AIR COMPRESSORS 151 

turn of the valve to its seat with precision and tightness. A small 
volume of air is compressed between valve and guide at the end 
of the lift, affording a cushion which removes shock without 
interfering with the quick action of the valve. The valve is free 
to turn and is self-grinding. The spiral spring is made of the 
proper pitch and strength to return the valve to its seat at the 
proper moment. 

Discharge valves of the poppet type are open to similar objec- 
tions as poppet inlet valves ; which has led to the introduction of 
mechanically moved valves of the Corliss and other types. 




Valve 




Fig. 36.— Air Valve of the Poppet Type. 



150. Mechanically Moved Discharge Valves. — When of the 
Corliss type, they are essentially of the same construction and 
are operated in the same manner as the valve illustrated in 
Fig. 34. 

The principal objection to positively operated discharge valves 
is, that the point of opening is fixed and thus too late when the 
discharge pressure is below, or .too early when above normal 
pressure, as this frequently happens with compressors supply- 
ing an intermittent demand. Such compressors, when using 
mechanically controlled discharge valves, have the latter usually 
arranged so that they are free to open automatically, but are 
positively closed. 

151. Fig. 37 shows such a valve, employed in some compressors 
built by the Allis Chalmers Co. As seen, the inlet valves are of 
the usual Corliss type; the discharge valves (A) open as soon as 
the air pressure in the cylinder reaches that of the air in the 
receiver and are positively closed by plungers (B), which are 
operated by being connected to a wrist plate driven by an eccen- 



152 



COMPRESSED AIR 



trie on the main shaft. The movement of the plunger is so timed 
as to positively bring the valves to their seat just as the piston 
reaches the end of the stroke, thus avoiding any slip of the air 
back by the valves. During the return stroke of the piston the 
valves are held to their seats by the discharge air pressure until 
the process is repeated on the succeeding forward stroke. In 
closing, the air between plunger and valve forms a cushion so 
that the valve is brought to its seat without noise or pounding. 

152. Fig. 38 shows an arrangement used in some compressors, 
built by the Nordberg Mfg. Co. Both inlet and discharge valves 



Bv*^^i 


^5S! 


1 


E. ^ I* 








■ M 

• «-• ■ 





Fig. 37. — Allis-Chalmers Discharge Valve. 

are of the Corliss type. In the center of each discharge valve are 
fitted a row of self-acting poppet valves, which open automatically 
when for any reason the discharge pressure is below normal. 

153. Corliss valves are not suited for discharge valves in single- 
stage compressors, compressing to more than 30 lb. gage, because 
the time between the opening and closing is too short to be per- 
formed by a positive mechanism. In such cases self-acting 
poppet valves are used. 

They may be used, however, in single-, two- or three-stage 
compressors, in which they have to be kept open during nearly 
one-half of the stroke. 

THE INTER-COOLER 

154. Inasmuch as the intercooler is the principal device by 
which a saving of power in stage compression is accomplished 
(see Article 57), it must be planned and designed so as to cool to 
initial temperature the heated air that passes through it on its 
way from one cylinder of a compressor to another. 



MECHANICAL FEATURES OF AIR COMPRESSORS 153 

To do this effectively, it must possess the following essential 
properties: 

1. The cooling surface offered to the circulating air must be 




Fig. 38. — A Nordberg Discharge Valve of the Corliss Type Fitted with 
Self-acting Poppet Valves. 

ample. This is generally based on the quantity of "free air" 
compressed per minute. 

2. The total volume should be as large as possible. Of two 
inter-coolers having the same amount of cooling surfaces, the 



154 



COMPRESSED AIR 



one of larger volume offers the advantage of allowing the air to 
be in contact with the cooling tubes for a longer period. 

3. The water-circulation should be planned so as to make the 
water flow unrestricted and with proper velocity through the 
pipes and thus absorb and carry away the maximum number of 
thermal units contained in the air. 

4. It should be provided with means for bringing the air in 
continuous contact with the cooling surfaces. This is usually 
accomplished by so-called " baffle plates." 

5. It should have convenient appliances for draining the con- 
densed moisture, and should permit easy access for inspection 
and repairs. 



WATER 
INLET* 




CONDENSATION DRAIN 

Fig. 39. — Section of Intercooler. 

155. Fig. 39 gives a sectional view of an inter-cooler built in 
accordance with modern practice. It consists of a cylindrical 
iron shell "A" containing a nest of tubes "B" through which 
cold water is circulated. The tubes are so spaced as to divide 
the air into thin sheets, and by means of baffle plates "C," the 
air is deflected and brought in contact with all parts of the cooling 
surface, before it leaves the inter-cooler. The tubes are expanded 
into tube sheets "D," and the rear tube sheet is covered by a 
head "E" which is in no wise connected to the shell but is free 
to slide within it, thus providing for any differences in expansion 
between shell and tubes. The rear end of the shell is closed by a 
separate head. The front head "F" can be removed and the 
tubes withdrawn for inspection and cleaning. The heads are 
provided on the inside with ribs, which abut against the tube 
sheets and compel the water to pass from end to end of the inter- 
cooler several times, thus obtaining the maximum cooling effect 
from a given quantity of circulating water. 



CHAPTER XIX 
COMPRESSOR ACCESSORIES 

156. The most essential accessories of a compressor plant are 
automatic regulators and receivers. Only a few types of each 
are illustrated and described in the following articles. They 
were selected at random, not with any intention of giving them 
preferences over other designs or makes, but merely to demon- 
strate how certain demands which are made on almost every 
compressor plant may be filled by mechanical means. 

AUTOMATIC REGULATORS 

157. In the industries using compressed air, particularly in 
mining operations, the consumption of air is often irregular and 
intermittent. For short periods it may cease entirely. 

To keep on compressing air when the demand is falling off 
would mean a waste of energy in that the surplus air would 
simply blow off through the safety valve of the receiver. To 
prevent such waste, compressors supplying an irregular demand 
are provided with so-called automatic regulators. 

Power-driven compressors, which must run at constant speed, 
and steam-driven, straight-line compressors which are liable to 
stick on centers when run below a certain speed, are usually 
provided with so-called "unloaders." 

Steam-driven, duplex compressors may use unloaders or speed 
governors, or a combination of both. 

158. Air Cylinder Unloaders. — These devices are designed to 
automatically shut off the supply of free air to the compressor 
when the consumption decreases. 

After shutting off the in-take, all the useful work ceases and 
only sufficient energy is expended to overcome friction of the 
moving parts. 

Fig. 40 shows an unloading device, built by the Union Steam 
Pump Co. It consists of a casing (a) and a plunger (b), which 
controls the admission of air into the compressor through the 

155 



156 



COMPRESSED AIR 



inlet pipe (c). Attached to one side of the casing is an auxiliary- 
piston (d), a lever (/) and a weight (g). 

The air pressure on the auxiliary piston is balanced by the 
weight which can be adjusted to unload the compressor at any 
desired pressure. When the decreased demand for air raises the 
pressure in the receiver beyond the normal, this increased pres- 
sure lifts the auxiliary piston (d), closes the port (h) and admits 
air at receiver pressure through port (m) under the plunger (b). 
The latter is thus raised and closes the air inlet pipe (c). 




tAir from 
Receiver 

Fig. 40. — Air Cylinder Unloader. 

When the receiver pressure falls to normal pressure again, on 
increased demand of air, piston (d) is pressed downward by 
weight (g), port (m) is closed, while the air confined under plunger 
(b) is exhausted into the atmosphere through port>(/i). Plunger 
(6) by its own weight drops into its first position, thus opening 
the main inlet pipe (c) and allowing the compressor to resume its 
useful work. 

159. Combined Speed Governor and Air-pressure Regulator. 
■ — In mining operations it happens at times that rock drills, 
hoists, pumps, etc., using air, are all started more or less simul- 
taneously, causing the compressor to run at an injurious speed to 
supply the unusual demand. At other times the demand may 
sink below the normal or cease altogether. 



COMPRESSOR ACCESSORIES 



157 



Compressors subject to such conditions are usually provided 
with a combined speed governor and pressure regulator. 

160. Fig. 41 shows such a device, furnished with certain com- 
pressors of the Ingersoll-Rand Co. This device consists of a 
regular fly-ball governor (a) with an auxiliary air cylinder (b) 
for holding a constant air pressure in the receiver. A casing (c) 
contains a special balanced throttle valve, the spindle of which is 
connected to the governor, the latter being belt- or chain-driven 




Fig. 41. — Ingersoll-Rand Combined Speed Governor and Air Receiver. 



from the compressor shaft. By this arrangement the steam 
supply is throttled when the speed exceeds the desired limit, 
which provides a safety stop against " runaway s" should an air 
pipe be broken. The piston in the air cylinder (b) presses against 
a weighted lever (e). This cylinder is connected by a small pipe 
(/) to the top of the air receiver. The inner end of the weighted 
lever connects with the spindle (d) of the balanced throttle valve 
through a link which makes the action of the air cylinder (b) 
independent of the governor (a). When the pressure in the 
receiver exceeds the normal, the weighted lever (e) is raised and 



158 COMPRESSED AIR 

the balanced throttle valve closed to a point which admits just 
enough steam to turn the machine over at the speed necessary to 
supply a volume of air equal to that drawn from the receiver. 

If, from any cause, the air pressure in the receiver diminishes, 
the weighted lever gradually drops, owing to the decrease of 
pressure in the small cylinder (6) . This action opens the throttle 
admitting more steam into the engine. Should an air pipe 
break, or should too great a demand be made upon the com- 
pressor, keeping the air pressure down so that the air piston does 
not perform the work, the machine will speed up to a point 
where the centrifugal governor partially closes the throttle, 
bringing the engine back to its rated full speed or the speed for 
which the governor is set. 

AIR RECEIVERS 

161. Air receivers have become indispensable accessories of 
every compressed-air installation. Since their design and size 
influence to a large extent the working of the whole system, the 
principal functions which they have to perform should be well 
understood. 

Receivers are used for three distinct purposes: 

1. To equalize the pulsations of the air coming from the com- 
pressor intermittently and to cause it to flow with a uniform 
velocity into the pipe line. Unless there is ample space for 
accommodating the air coming from the compressor, the pressure 
will run up momentarily in excess of the normal, thus throwing 
unnecessary strain on the machine and consuming extra power. 

Receivers are employed to provide this space and in order to 
perform this function effectively, they should be placed within 
a few feet of the compressor and connected with it by a pipe of 
sufficient size. 

2. To keep the friction of air in the pipe line as small and as 
uniform as possible, thereby preventing a loss of energy. In 
Article 100 it has been shown that friction increases with velocity 
and the latter increases with the difference of pressure at both 
terminals of the pipe line. It is therefore important to keep this 
difference as small and as uniform as possible. In a long line this 
is best accomplished by placing another receiver at the end of the 
line, close to the air engine. Just as a receiver near the com- 
pressor prevents the rise of pressure above the normal when 



COMPRESSOR ACCESSORIES 



159 



air is forced into the pipe, one at the end of the line will pre- 
vent a sudden fall of pressure below the normal when air is 
quickly withdrawn from the pipe line. 

3. To collect the moisture and grease which the air carries in 
suspension and which would otherwise be carried into the pipe line 
by the force of the current. By allowing the heated air to pause 
in its flow through the receiver, it is cooled and will therefore drop 
most of the water and the oil, which at proper intervals are dis- 
charged through suitable drain pipes. 

A receiver, unless made of prohibitory size, can never act as a 
reservoir for compressed air, because upon withdrawing air from 




Fig. 42. — Air Receivers. 



it, the pressure falls so rapidly that even if of huge dimensions, a 
receiver could supply the demand only for a few minutes, should 
the compressor stop for that period of time. 

In order to fill the legitimate requirements pointed out above, 
the dimensions of a receiver must conform to the capacity of the 
compressor and the discharge pressure of the air. What these 
dimensions should be for any individual installation is a matter 
that has been determined largely by experiment. 

Compressor manufacturers usually furnish receivers to go with 
a compressor of given capacity and list in their catalogues the 



160 



COMPRESSED AIR 



proper size of a receiver corresponding to the output of the 
compressor in cubic feet of free air per minute. 

Air receivers are built either horizontal or vertical. They are 
cylindrical vessels made of sheet steel of large tensile strength. 
The girth seams are single, and the side seams double-riveted. 
A manhole is provided for inspection and repairs. 

Each receiver is usually provided with a pressure gage, a safety 
valve and a blow-off cock. 

Fig. 42 shows a vertical and a horizontal receiver built by the 
Sullivan Machinery Co. 

162. After-coolers. — Inasmuch as they perform practically 
the same function as an inter-cooler, they are usually of the same 
or very similar construction as the inter-cooler shown in Fig. 39. 
They are sometimes employed in place of an ordinary receiver 
in order to realize more fully the saving of power that results 
from the partial cooling of the air in the receiver. Such cooling 
reduces the momentary increase of pressure due to the heat of 
compression and as a consequence diminishes the power required 
in forcing the air out of the compressor cylinder into the receiver. 

They also secure a more complete cooling of the air before it 
enters the pipe line, and therefore a more perfect extraction of 
moisture and grease carried in suspension by the heated air. 



APPENDIX. 

TABLES I TO IX 



APPENDIX 



161 



03 
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tf 
P 

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P4 
W 
P-. 

3 

H 
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CO 

o » 

i-i rt 

Ph o 

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C_i co 

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162 



COMPRESSED AIR 



TABLES 



TABLE II.— VOLUME IN CUBIC FEET OF 1 LB. OF AIR AT ATMOSPHERIC 
PRESSURE AT SEA LEVEL AND AT VARIOUS TEMPERATURES 



Degrees 
Fahr. 



Volume at atmos. pressure 



Cubic feet 
in 1 lb. 



Comparative 
volume 



Degrees 
Fahr. 



Volume at atmos. pressure 

Cubic feet j Comparative 

in 1 lb. volume 






11.583 


.881 


130 


14 . 846 


1.130 


32 


12.387 


.943 


140 


15.100 


1.149 


40 


12.586 


.958 


150 


15.351 


1.168 


50 


12.840 


.977 


160 


15.603 


1.187 


62 


13.141 


1.000 


170 


15.854 


1.206 


70 


13.342 


1.015 


180 


16.106 


1.226 


80 


13.593 


1.034 


200 


16.606 


1.264 


90 


13.845 


1.054 


210 


16.860 


1.283 


100 


14.096 


1.073 


212 


16.910 


1.287 


110 


14.344 


1.092 


220 


17.128 


1.301 


120 


14.592 


1.111 









APPENDIX 



163 



TABLE III.— VOLUMES, MEAN PRESSURES PER STROKE, AND FINAL TEM- 

PERATURES IN AIR COMPRESSION AT SEA LEVEL 

(Initial temperature = 60° Fahr.) 



1 


2 


3 


4 


5 


6 


7 


8 


Gage 
pressure 


Abso- 
lute 
pressure 


Atmos- 
pheres 


Volume 

of air 
isother- 
mal com- 
pression 


Volume 
of air 
adia- 
batic 
com- 
pression 


Mean 

pressure 

per 

stroke 
isother- 
mal com- 
pression 


Mean 
pressure 

per 

stroke 

adiabatic 

com- 
pression 


Final 
tempera- 
ture, 
degrees 
Fahr. 
adiabatic 
compres- 
sion 


Gage 
pressure 





14.7 


1. 


1. 


1. 


0. 


0. 


60 





5 


19.7 


1.34 


.7462 


.81 


4.3 


4.5 


106 


5 


10 


24.7 


1.68 


.5952 


.69 


7.62 


8.27 


145 


10 


15 


29.7 


2.02 


.495 


.606 


10.33 


11.51 


178 


15 


20 


34.7 


2.36 


.4237 


.543 


12.62 


14.4 


207 


20 


25 


39.7 


2.7 


.3703 


.494 


14.59 


17.01 


234 


25 


30 


44.7 


3.04 


.3289 


.4638 


16.34 


19.4 


25.3 


30 


35 


49.7 


3.381 


.2957 


.42 


17.92 


21.6 


281 


35 


40 


54.7 


3.721 


.2687 


.393 


19.32 


23.66 


302 


40 


45 


59.7 


4.061 


.2462 


.37 


20.52 


25.59 


321 


45 


50 


64.7 


4.401 


.2272 


.35 


21.79 


27.39 


339 


50 


55 


69.7 


4.741 


.2109 


.331 


22.77 


29.11 


357 


55 


60 


74.7 


5.081 


.1968 


.3144 


23.84 


30.75 


375 


60 


65 


79.7 


5.423 


.1844 


.301 


24.77 


31.69 


389 


65 


70 


84.7 


5.762 


.1735 


.288 


26. 


33.73 


405 


70 


75 


89.7 


6.102 


.1639 


.276 


26.65 


35.23 


420 


75 


80 


94.7 


6.442 


.1552 


.267 


27.33 


36.6 


432 


80 


85 


99.7 


6.782 


.1474 


.2566 


28.05 


37.94 


447 


85 


90 


104.7 


7.122 


.1404 


.248 


28.78 


39.18 


459 


90 


95 


109.7 


7.462 


.134 


.24 


29.53 


40.4 


472 


95 


100 


114.7 


7.802 


.1281 


.232 


30.07 


41.6 


485 


100 


' 105 


119.7 


8.142 


.1228 


.2254 


30.81 


42.78 


496 


105 


110 


124.7 


8.483 


.1178 


.2189 


31.39 


43.91 


507 


110 


115 


129.7 


8.823 


.1133 


.2129 


31.98 


44.98 


518 


115 


120 


134.7 


9.163 


.1091 


.2073 


32.54 


46.04 


529 


120 


125 


139.7 


9.503 


.1052 


.202 


33.07 


47.06 


540 


125 


130 


144.7 


9.843 


.1015 


.1969 


33.57 


48.1 


550 


130 


135 


149.7 


10.183 


.0981 


.1922 


34.05 


49.1 


560 


135 


140 


154.7 


10.523 


.095 


.1878 


34.57 


50.02 


570 


140 


145 


159.7 


10.846 


.0921 


.1837 


35.09 


51. 


580 


145 


150 


164.7 


11.204 


.0892 


.1796 


35.48 


51.89 


589 


1 50 



164 



COMPRESSED AIR 



TABLE V 


—THEORETICAL HORSE-POWER AND FINAL TEMPERATURES 




(Initial temperature 


= 60 


°Fahr. 


at sea level) 










Single-stage 






















compression 
























Two-stage 


Three-stage 


Four-si 
















Iso- 




compression 


compression 


compression 






ther- 


Adiabatic 






















mal 






















3* 

03 -j 


*2 


la 




-a 


"3 


03 

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T3 

a & 


"3 

a 


03 

03 d 


T3 
2 03 


"3 

a 


S a 
^'5 


03 

I 

m 


03 

03 

(H 

03 
43 


03 ^ 

s'a 

o u 

1! 
is 

03 
03 ° 


id .a 

a2 

as 

-S-3 

03 03 


43 
o 

O 

03 
U 

a 


43 
c3 
fa 

03 

03 

03 
U 

W) 
<13 
T3 
03 
U 
d 


s.a 

ss 

O ft 
° u 

H3 03 

u £ 


u 

03 
43 

O 

03 

o 
£ 

ft 


a 03 

. 03 

S- U 

03 O 
03 

£?3 

-2.40 


s.a 

03 rf 

ag 

o a 

° u 

S'3 

T3 0) 

03 03 


03 

43 

O 
03 

O 

T3 

a 


03 03 
ft 03 
.03 

^ g. 

«a 

fe o 

03 W 
03 o 

£•1 
till 03 
03^2 
T3 o3 


03 3 

s a 
as 

Oft 

°*i 

"d 03 
03 03 


03 

43 

O 

03 

O 
^> 

T3 

03 

u 

03 
ft 


03 S 
ft 03 

^a 
03 « 

8.s 

£3 


03 
bC 

O 


03 

o 

a 


d . 

to'** 


o 
o 

c3 


c3 
03 

a 

S 


d . 
u . 

n d 
5 o 


a 

O 

o 

03 

03 


03-2 
"3 M 


d . 

03 <+■> 

k d 

03 O 


d 
o 
o 

03 


d * 

2 fl 


d . 

03«*H 

u d 

03 03 


a 

o 

03 
73 

03 


0)T3 






£rH 


£t-< 


>> 




fc-l 


>> 


a-^ 


*rH 


>> 


a S 


^^H 


>> 


a o 
IS 






a* 

7*03 

03 > 

03 --H 


O u 

ag 
03J3 

E*03 

W 


(3 

.2 
'8 


"3 

d 


1 03 

w 73 


o 

a 

03 

'o 


a ° 
1 ? 

"c8 ° 

fid 


O 

a *-> 
r 03 

03 > 
03 .-h 

w 73 


d 
.2 

1 


03 ^ 
^ 03 

1.2 


o 

ft U 
1 03 
«_> 

°^ 

W^ 3 


d 
.2 


5 


1.34 
1.68 
2.02 
2.36 
2.70 
3.04 
3.72 
4.40 
5.08 
5.76 
6.44 
7.12 
7.80 
8.48 
9.16 
9.84 
10.52 
11.20 
11.88 
13.24 
14.60 
16.3 
18. 
19.7 
21.4 
24.8 
28.2 
31.6 
35. 


.0188 
.0333 
.0481 
.0551 
.0638 
.0713 
.0843 
.0948 
.1037 
.1120 
.1196 
.1260 
.1320 
.1371 
.1422 
.1467 
.1510 
.1547 
.1583 
.1656 
.1720 
.1790 
.1860 
.1920 
.1970 
.2060 
.2140 
.2230 
.2290 


.0197 

.0362 

.0505 

.0630 

.075 

.085 

.104 

.120 

.134 

.148 

.16 

.171 

.182 

.192 

.202 

.210 

.218 

.226 

.234 

.249 

.263 

.278 

.292 

.306 

.317 

.342 

.364 

.381 

.398 


.96 
.93 
.90 
.88 
.85 
.84 
.81 
.79 
.77 
.75 
.74 
.74 
.73 
.72 
.71 
.70 
.69 
.69 
.68 
.67 
.65 
.64 
.64 
.63 
.62 
.60 
.59 
.58 
.57 


106 
145 
178 
207 
234 
252 
302 
339 
375 
405 
432 
459 
485 
500 
529 
560 
570 
589 
607 
640 
672 
715 
749 
780 
815 
867 
915 
960 
1000 




















10 




















15 




















20 




















25 




















30 




















40 




















50 


.109 
.121 
.131 
.141 
.150 
.158 
.165 
.172 
.179 
.186 
.193 
.198 
.208 
.217 
.227 
.237 
.247 
.256 
.272 
.283 
.295 
.307 


.87 
.86 
.85 
.85 
.84 
.83 
.83 
.83 
.82 
.82 
.81 
.81 
.80 
.79 
.79 
.78 
.78 
.77 
.76 
.76 
.75 
.75 


188 
203 
214 
224 
234 
243 
250 
257 
265 
272 
279 
285 
297 
309 
320 
331 
342 
352 
370 
380 
397 
415 














60 














70 














80 














90 














100 














110 














120 














130 














140 














150 


.182 
.187 
.197 
.206 
.215 
.224 
.233 
.241 
.252 
.262 
.272 
.282 


.85 

.85 
.84 
.83 
.83 
.83 
.82 
.82 
.82 
.82 
.82 
.81 


200 
204 
211 
218 
224 
230 
236 
241 
250 
258 
266 
275 








160 








180 








200 








225 








250 








275 








300 








350 








400 








450 








500 


.26 


.88 


215 


550 


38.4 


.2340 


.416 


.56 


104C 


.321 


.73 


430 


.292 


.80 


283 


.269 


.87 


220 


600 


41.8 


.240 


.432 


.55 


1077 


.332 


.72 


442 


.300 


.80 


290 


.278 


.86 


225 


650 


45.2 


.245 


.447 


.55 


1113 


.345 


.71 


451 


.31 


.79 


295 


.284 


.86 


228 


700 


48.6 


.249 


.461 


.54 


1136 


.355 


.70 


458 


.32 


.78 


300 


.29 


.86 


234 


750 


52. 


.252 


.475 


.53 


1178 


.363 


.69 


462 


.327 


.78 


305 


.296 


.85 


236 


800 


55.4 


.258 


.488 


.52 


1208 


.373 


.69 


468 


.334 


.78 


309 


.302 


.85 


240 


850 


58.8 


.262 


.500 


.52 


1237 


.381 


.69 


480 


.341 


.77 


314 


.307 


.85 


244 


900 


62.2 


.265 


.512 


.52 


1265 


.388 


.68 


490 


.347 


.76 


319 


.312 


.85 


247 


950 


65.6 


.268 


.523 


.51 


1292 


.395 


.68 


495 


.354 


.76 


322 


.316 


.85 


250 


1000 


69. 


.272 


.534 


.51 


1318 


.403 


.67 


498 


.360 


.75 


325 


.32 


.85 


252 


1100 


75.8 


.278 


.555 


.50 


1367 


.416 


.67 


507 


.370 


.75 


331 


.327 


.85 


254 


1200 


82.6 


.283 


.575 


.49 


1415 


.429 


.66 


525 


.381 


.74 


338 


.334 


.84 


258 


1300 


89.4 


.289 


.594 


.49 


1457 


.441 


.66 


534 


.390 


.74 


342 


.341 


.84 


265 


1400 


96.2 


.293 


.611 


.48 


1498 


.452 


.65 


550 


.399 


.74 


349 


.348 


.84 


270 


1500 


103. 


.297 


.627 


.48 


1537 


.462 


.65 


563 


.406 


.73 


353 


.355 


.84 


273 


1600 


109.8 


.301 


.643 


.47 


1575 


.472 


.64 


568 


.415 


.73 


358 


.361 


.83 


276 


1700 


116.6 


.305 


.659 


.47 


lfilC 


.482 


.63 


589 


.424 


.72 


364 


.367 


.83 


280 


1800 


123.4 


.309 


.673 


.46 


1645 


.491 


.63 


606 


.431 


.72 


370 


.372 


.83 


284 


1900 


130.2 


.313 


.687 


.46 


167S 


.500 


.63 


628 


.438 


.72 


374 


.377 


.83 


287 


2000 


139. 


.317 


.701 


.45 


1709 


.509 


.62 


639 


.444 


.71 


378 


.381 


.83 


290 


2250 


154. 


.324 


.733 


.44 


1784 


.528 


.62 


645 


.460 


.70 


385 


.393 


.82 


294 


2500 


171. 


.331 


.763 


.43 


1852 


.547 


.61 


654 


.474 


.70 


398 


.405 


.82 


298 


3000 


205. 


.342 


.816 


.42 


1975 


.579 


.59 


670 


.500 


.69 


414 


.42 


.81 


308 


1 


1 2 1 3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 






APPENDIX 



165 



TABLE IV.— VOLUME WHICH 1 CU. FT. OF FREE AIR, HAVING A TEMPERA- 
TURE OF 60° FAHR., WILL OCCUPY WHEN COMPRESSED IN ONE 
STAGE ADIABATICALLY TO VARIOUS ATMOSPHERES 

Also final temperature of the air at such pressures 



1 


2 


3 


4 


Pressure in atmos- 


Absolute pressures 


Volumes in cu. ft. 


Final temp., degrees 


pheres 


in lb. per. sq. in. 


adiab. comp. 


Fahrenh. 


1.00 


14.70 


1.000 


60.0 


1.25 


18.37 


0.854 


94.8 


1.50 


22.05 


0.750 


124.9 


2.00 


29.40 


0.612 


175.8 


2.50 


36.70 


0.522 


218.3 


3.00 


44.10 


0.459 


255.1 


3.50 


51.40 


0.411 


287.8 


4.00 


58.80 


0.374 


317.4 


5.00 


73.50 


0.319 


369.4 


6.00 


88.20 


0.281 


414.5 


7.00 


102.90 


0.252 


454.5 


8.00 


117.60 


0.229 


490.6 


9.00 


132.30 


0.211 


523.7 


10.00 


147.00 


0.195 


554.0 


15.00 


220.50 


0.147 


681.0 



TABLE VI.— MULTIPLIERS FOR DETERMINING THE VOLUME OF FREE AIR 
AT VARIOUS ALTITUDES WHICH, WHEN COMPRESSED TO VARIOUS 
PRESSURES, IS EQUIVALENT IN EFFECT TO A GIVEN VOLUME OF 
FREE AIR AT SEA LEVEL 





Barometric pressure 


Multiplier 


Altitude 
in feet 


Inches of 
mercury 


Pounds per 
square inch 


Gage pressure (pounds) 


60 


80 


100 


125 


150 





30.00 


14.75 


1.000 


1.000 


1.000 


1.000 


1.000 


1,000 


28.88 


14.20 


1.032 


1.033 


1.034 


1.035 


1.036 


2,000 


27.80 


13.67 


1.064 


1.066 


1.068 


1.071 


1.072 


3,000 


26.76 


13.16 


1.097 


1.102 


1.105 


1.107 


1.109 


4,000 


25.76 


12.67 


1.132 


1.139 


1.142 


1.147 


1.149 


5,000 


24.79 


12.20 


1.168 


1.178 


1.182 


1.187 


1.190 


6,000 


23.86 


11.73 


1.206 


1.218 


1.224 


1.231 


1.234 


7,000 


22.97 


11.30 


1.245 


1.258 


1.267 


1.274 


1.278 


8,000 


22.11 


10.87 


1.287 


1.300 


1.310 


1.319 


1.326 


9,000 


21.29 


10.4B 


1.329 


1.346 


1.356 


1.366 


1.374 


10,000 


20.49 


10.07 


1.373 


1.394 


1.404 


1.416 


1.424 



166 



COMPRESSED AIR 



TABLE VII. 



-EFFECT OF INITIAL OR IN-TAKE TEMPERATURE ON EFFI- 
CIENCY AND CAPACITY OF AIR COMPRESSORS 





Unit capacity and efficiency assumed at 60° Fahr. 




Initial temperature 


Relative capacities 
and efficiencies 


Initial temperature 


Relative capaci- 


Degrees 
Fahr. 


Degrees 
Abs. 


Degrees 
Fahr. 


Degrees 

Abs. 


ties and effi- 
ciencies 


-20 


441 


1.18 


70 


531 


0.980 


-10 


451 


1.155 


80 


541 


0.961 





461 


1.13 


90 


551 


0.944 


10 


471 


1.104 


100 


561 


0.928 


20 


481 


1.083 


110 


571 


0.912 


30 


491 


1.061 


120 


581 


0.896 


32 


493 


1.058 


130 


591 


0.880 


40 


501 


1.040 


140 


601 


0.866 


50 


511 


1.020 


150 


611 


0.852 


60 


521 


1.000 


160 621 


0.838 



Adiabatic Compression and Delivery: 

TABLE VIII.— THEORETICAL H.P. FINAL VOLUME AND FINAL ABSOLUTE 

TEMPERATURE 



No. of 

stages 



Theoretical horse power 



Final volume 
in cubic feet 



Final absolute 
temperature 



1 

stage 



144/iP, 



33,000( 



^fe^-J I y>-r. ST™ 



^ —=0-29 



stage 2 



l^nP a V a Lp*^ 1 sPa-^-P- =0-856 p !^i =0.144 

$.000(7*- DLL? J J 2 Va \P-2J 2 a \Pa) 



33, 000 ( 



3 

stage i 


144nP a F„ [/Psx^ J 
33,000(n-l)LVpJ J 


/P , 2 \ +1 - 0.9037 


.P^ 7 ^ =0.0963 

T3= Hk) 3n 


4 
stage 


144nP a Fa \ (Piy^T A 
33,000(n-l) LVpJ J 


/Pa , 3 ' l t l -0-9278 


.p.. ^fi =0.0722 



APPENDIX 



167 



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INDEX 



(Figures refer to number of article) 



Absolute pressure, 11 
temperature, 10 
zero, 9 
Adiabatic compression and expan- 
sion, 14 
compression curve, 43 
compression, graphic illustra- 
tion, 42 
horse power, 47, 48, 50 
mean gage pressure, 46 
theory of, 40 
work per stroke, 44, 45 
compression, relation between 
volume, pressure and tem- 
perature, 41 
Advantages of stage compression, 75 
After cooler, 162 

Air card, single stage compression, 83 
two stage compression, 84, 85 
composition of, 1 
compressed in compressors, 25, 

29 
compressors, 126 
cylinder, 25 

unloaders, 158 
cylinders, dimensions of, 63, 64, 

65,66 
engines, 106, 116 
indicator card, 82, 85 
inlet valves, 27, 144, 145, 146, 

147 
pressure regulator, 159 
receiver, 161 
re-heaters, 123, 124, 125 
used with complete expansion, 
110 
partial expansion, 113 
weight of, 2, 21, 23, 24, 24a 
Altitude, compression at, 77, 78, 79 
effect of on transmission, 97 



Altitude, effect of on pipe line effi- 
ciency, 102 
how calculated, 4 
multipliers for computation, 78 
power required for compression 

at, 79 
volumetric efficiency at, 77, 81 
Atmospheric pressure, 3 

how calculated, 4 
Atmosphere, work performed by in 
compression and delivery, 
33, 117 
Automatic regulators, 29, 157 



B 



Belted, compared with steam driven 

compressors, 137 
Belt driven compressors, 137, 138 

two stage compressor, 138 
Bends in air pipes, 99 
Boyle's law, 15, 16 
Boyle's and Charles' laws combined, 

20 
Branch pipes, dimensions of, 98 
British Thermal Unit, 6 



.Capacity affected by intake air, 54 
throttling of intake air, 87 
of compressor, 54 
of compressor affected by clear- 
ance, 54 
Charles' law, 17, 18, 19 
Choking of air pipes by ice, 104 
Clearance, 51 

effect of on power consumption, 

50, 52 
effect of on volumetric efficiency, 

50 
losses due to, 52 



169 



170 



INDEX 



Compound compression, 25, 57 
advantages of, 75 
at altitudes, 80 
ratio of compression in, 59 
when used, 76 
Compressed air drills, 109 
air, reheating of, 122 

indicator cards, 82, 85 
air installation, efficiency of, 

121 
air used with complete expan- 
sion, 110, 111 
partial expansion, 113, 114, 
115 
Compression of air in compressors, 

25, 29 

work all converted into heat, 

117 
Compressor speed, 55 
Construction of pipe line, 104 
Conveyance of compressed air, 91, 

105 
Cooling of air during compression, 

26, 57 

water required in air compres- 
sion, 86 
Cylinder diameters of compressors, 
63 
four stage compressor, 66 
three stage compressor, 65 
two stage compressor, 64 



Diameters of air cylinders, 63, 64, 

65, 66 
Dimensions of pipe line, 95, 103 
Discharge valves, 27, 148, 153 
Dry air, specific heat of, 8 
Dryer air in compound compression, 

75 
Duplex compressors, 127 

disadvantages of, 131a 
steam-driven compressor, opera- 
tion of, 131 
single stage compressor, 132 
two stage compressor, 133, 
134 



E 

Efficiency of air used at full pressure, 
109 
compressor plant, 87 
pipe line, 101, 102 
compressed air installation, 121 
pipe line affected by altitude, 
102 
Elbows in pipe lines, 99 
Electrically driven compressors, 140 
geared, two-stage compressor, 

141 
direct-connected, two-stage com- 
pressor, 141, 142 
Energy in air after abstraction of 

heat, 117 
Expansion of air, adiabatic, 14 

isothermal, 13, 39 
Explosion preventives, 90 
Explosions due to throttling devices, 
89 
in air compressors, 75, 88 



Final temperature of compressed air, 

41, 41a 
Flow of compressed air in pipes, 92 
of compressed air from an ori- 
fice, 105 
Four stage compressor, cylinder di- 
ameters, 66 
stage compression, ratio of, 62 
Free air, 12 

Freezing of moisture contained in 
compressed air, 75e, 104 
prevented by re-heating, 122 
Friction losses in air compression, 50 
engines, 116 
pipes, 92 

affecting power con- 
sumption, 50, 56 
Fuel cost of re-heating, 122 



Gage pressure, 11 
Gay Lussac's law, 17 
Governors, speed, 159, 160 






INDEX 



171 



Graphical illustration of isothermal 
compression, 31 
adiabatic compression, 42 



H 



Heat of compression, 61 

general effect of on air, 5 

loss, effect of, 117 
Horse power, adiabatic compression 
and delivery, 47, 50 

of air engines using air with par- 
tial expansion, 115, 116 

of four-stage adiabatic compres- 
sion and delivery, 71, 74 

of single-stage isothermal com- 
pression and delivery, 37, 
50 

of three-stage adiabatic com- 
pression and delivery, 70, 74 

of two-stage adiabatic compres- 
sion and delivery, 68, 69, 74 



Indicator cards, 82, 83, 84, 85 

Ingersoll-Rogler valve, 147 

Inlet valves, 27, 144, 145, 146 

Inter cooler, 57, 154, 155 

Internal or intrinsic energy of air, 
118, 119, 120 

Isothermal compression, 13, 30, 31 
curve, equation of, 32 
horse power, 37 
mean gage pressure, 36 
not attainable in practice, 38 
work per stroke, 33, 34, 35 
expansion, 13, 39 
horse power, 39 



Joule's law, 118 



Laidlaw-Dunn-Gordon compressor, 

132 
Leaks in compressor cylinder, cause 
of explosion, 88 
pipe line, 104, 105 



Leaky air pistons, effect on air card, 
82 
discharge valves, effect on air 

card, 82 
inlet valves, effect on air card, 
82 
Loss of capacity due to throttling of 
inlet air, 53, 87 
of energy due to loss of heat, 87 
of energy due to leaks, 87 
pressure in pipe line, 93 
power in pipe line, 94 
due to clearance, 52 
volumetric efficiency due to 
clearance, 52 
Losses due to heating of intake air, 

87, 121 
Lubrication, 26, 75 

M 

Mean gage pressure, isothermal single 
stage compression and deliv- 
ery, 36 
gage pressure, adiabatic single 
stage compression and de- 
livery, 46 
gage pressure, two-stage com- 
pression and delivery, 72 
three-stage compression and de- 
livery, 73 
at partial expansion, 114 
Mechanically controlled air valves, 

27, 146 
Mechanical details of compressors, 
143 
' efficiency of compressor, 56, 87 
Moisture in air, effect of on specific 

heat, 8 
Multipliers for altitude computa- 
tion, 78 
Multi-stage compression, 25, 57 
advantages of, 75 
at altitudes, 80 
when to use, 76 

N 

"n," value of, 40, 117a 
Nordberg compressor, 141 
Norwalk compressors, 138, 139 



172 



INDEX 



O 

Oils, lubricating, 88, 90 



Pipe line construction, 104 
computation formulas, 96 
dimensions affected by altitude, 

97 
dimensions, 95, 103 
effect of leaks in, 104, 105 
efficiency, 101 

affected by altitude, 102 
loss of pressure in, 93 
power in, 94 
Piston displacement, 51 

speed of compressor, 55 
Poppet valves, 27, 145 



Speed, increasing difficulty in lubri- 
cation, 55 
governor, 159 
Stage-compression, 57 
advantages of, 75 
at altitudes, 80 
increased safety in, 75 
when used, 76 
ratio of compression in, 59 
Steam-driven compressors, 127, 135 
Steam economy in stage compression, 

75 
Straight-line compressors, 127 

steam-driven compressors, 
operation of, 128 
single stage compressor, 129 
two stage compressor, 130 
Sullivan compressors, 129, 130 



Rating of compressors, 54 
Ratio between final pressure and 
power required, 49 
of compression in two-stage 
compressors, 60 
in three-stage compressors, 61 
in four-stage compressors, 62 
in compound compressors, 59 
Receiver pressure, 29 
Receivers, 161 

Regulators, automatic, 29, 157 
Re-heaters, 123, 124, 125 
Re-heating of compressed air, 122 

to increase efficiency, 121 
Rock drills, 109 
Rope driven compressor, 140 



Single stage compression, 25, 28 

compression air card, 83 
Specific heat, 6 

of air at constant volume, 7 
pressure, 8 
Speed of compressors, 155 

affecting volumetric efficiency, 
55 



Temperatures, adiabatic compres- 
sion and expansion, 41 
causes of abnormal, 88 
in compound compression, 75 
Temperature of intake air affecting 
power required to compress, 
54 
losses due to, 54, 87 
Thermal cost of re-heating, 122 
Thermodynamic laws applied to air 
compression and expansion, 
6, 41a, 117 
Three-stage compression, ratio of 
compression, 61 
cylinder diameters, 65 
Throttling devices causing explo- 
sions, 89 
Transmission of air affected by alti- 
tude, 97 
compressed air, 91, 105 
Two stage compression, 25, 57, 58, 
60 
air card, 84, 85 
ratio of compression, 60 
cylinder diameters, 64 

U 

Unloaders, air cylinder, 158 



INDEX 



173 



Valves in air pipes, 104 
Velocity of air in pipe line, 100 
Volumetric efficiency affected by 
clearance, 52 
efficiency, 53, 87 

in stage compression, 53, 67, 75 
affected by restricted inlet 

area, 53, 82, 87 
at altitudes, 81 



W 

Water jackets, 26, 57 

required for cooling, 86 
wheel dri-ven compressor, 139 

Weight of air, 2, 21, 22, 23, 24, 24a 



Zero, absolute, 9 



